The Mathematica Guidebooks

# Index of the GuideBooks

Symbols, A-C | D-E | F-H | I-J | K-M | N-P |Q-S | T-W | X-Z | Download index (1.5 MB .pdf)

## F

Faà di Bruno formula S.1.Sol.17

`FaceForm` G.2.1.2

`FaceGrids` G.2.1.3

Faces

• of 3D Platonic solids G.2.1.5
• of a 120-cell G.2.Ex.17
• of Mathematica P.1.2.0
• of polygons G.2.1.2
• of polyhedra G.2.Ex.16

`Factor` P.3.1.1, S.1.2.1

`FactorComplete` N.2.1

`Factorial` N.2.3, S.1.Ex.30

Factorial

• digits of ~s N.2.3
• function P.1.2.4, N.2.3
• user-defined P.1.2.4

`Factorial2` N.2.3

`FactorialBaseForm` N.2.Sol.5

`FactorialPrimeDecomposition` N.2.Sol.17

`FactorInteger` N.2.1

Factorization

• complexity of integer ~ N.2.1
• of cyclotomic polynomials S.1.Ex.1
• of factorials N.2.Ex.17
• of integers N.2.1
• of polynomials P.3.1.1, S.1.2.1
• of random polynomials S.1.2.1
• of trigonometric expressions P.3.1.1, S.1.4
• optical ~ N.2.Sol.12
• over extension fields S.1.2.1

Factors

• for Mathematica P.1.Sol.2
• of factorials N.2.Sol.17
• of integers N.2.1
• of polynomials P.3.1.1, S.1.2.1

Failed, assignments P.3.1.1, P.4.3.2, P.5.2.2

Failing, operations P.4.1.1

Faithfulness, of Riemann surfaces N.1.11.2

Falling

• ball P.1.Sol.1
• buttered toast P.1.Sol.1
• cat P.1.Sol.1
• coin P.1.Sol.1
• leaves P.1.Sol.1, P.1.Sol.1
• stone N.1.2, S.1.7.1

`False` P.5.1.1

False

• functions returning True or ~ P.5.1.1
• the truth value ~ P.5.1.1

Family names, distribution of ~ P.1.Sol.1, P.6.Ex.4

`FancyPlatonicSolid` G.2.Sol.1

FAPP-function S.1.Ex.32

Farey

• fractions G.1.1.1, G.1.2.2
• sequence N.1.8, N.2.2, N.2.Ex.10
• set G.1.1.1
• tree G.1.1.1

Farey-Brocot sequence G.1.1.1, N.2.Ex.10

`FareyBrocotMeasure` N.2.Sol.10

`FareyBrocotUnion` N.2.Sol.10

Fefferman-de la Llave decomposition S.3.Ex.1

Fejér sum S.2.4

FEM S.1.Ex.7

Fermat numbers S.1.9.2

Fermat test S.1.Ex.20

Fermi-Dirac integral N.1.10.1, S.3.Ex.11

Ferrer

• conjugates P.5.Ex.9, P.6.Ex.21
• diagrams P.5.Ex.9

`FerrerConjugate` P.6.Sol.21

FeynCalc In, P.1.2.4

FFT N.1.5

`Fibonacci` N.2.4

Fibonacci

• basis N.2.Ex.13
• chain map P.2.4.2
• coefficients N.2.4
• function N.2.4
• identities S.3.1
• matrix eigenvalues N.1.4
• numbers N.2.4, N.2.Ex.13
• random ~ recursion N.1.1.1, N.1.3
• sums S.1.6.4
• andomized ~ iterations N.1.3

Fibonacci-Binomial theorem N.2.4

Field

• electric ~ G.1.4, G.3.Ex.12, N.1.3, N.1.11.1
• electromagnetic ~ S.3.Ex.20
• electromagnetic ~ under a Lorentz transformation P.6.5.1
• electrostatic ~ G.1.Sol.4, G.3.3, N.1.3, N.1.11.1, S.3.6
• extension ~ S.1.2.1
• force-free magnetic ~ S.3.Ex.20
• in a metallic cone S.3.6
• invariants P.6.5.1
• knotted ~ configurations P.1.Sol.1
• lines P.1.2.3, G.1.4, N.1.11.1
• magnetic ~ P.1.2.3, N.1.8, N.1.11.1
• magnetostatic ~ N.1.11.1
• particle in a ~ P.1.2.3
• strength tensor P.6.5.1
• transformations P.6.5.1, S.1.Ex.29

Field lines

• electric ~ N.1.11.1
• knotted ~ N.1.11.1
• magnetic ~ P.1.Sol.1, N.1.11.1
• randomized ~ G.2.Sol.1
• wiggly ~ G.2.Sol.1

`Fifteen` N.2.Sol.9

Figures

• impossible ~ G.2.3.6
• random ~ with smooth boundaries G.1.Ex.15
• random animated ~ G.1.Ex.15
• touching ~ G.1.Ex.15
• various 2D ~ G.1.1.1
• various 3D ~ G.2.Sol.1

File operations P.4.4.1

`FileNames` P.6.6

Files

• deleting ~ P.4.4.1
• names of ~ P.6.6
• operations on ~ P.4.4.1
• reading from ~ P.4.4.1, P.6.6
• saving definitions to ~ P.4.4.1
• saving to ~ P.4.4.1

Filling

• bins N.2.Ex.17
• jugs P.1.Sol.1
• lists P.6.3.3
• seeded matrices N.1.Ex.32

Filters N.1.5

`FindMinimum` N.1.9

`FindRoot` N.1.8

Finite

• difference weights P.5.Ex.7
• dimensional representation of CCR S.1.2.2
• element method S.1.Ex.7
• expressions for divergent sums S.1.8
• fields N.2.1
• length solitons S.1.8
• part S.1.8
• parts of divergent integrals S.1.6.2
• parts of divergent products S.3.Ex.15
• parts of divergent sums S.1.6.6, S.1.8
• sums S.1.6.6

`FiniteStraightWirephi` N.1.11.1

`First` P.6.3.1

First

• digits in calculations N.1.Ex.33
• digits of data P.6.Ex.1
• element of expressions P.6.3.1
• element of lists P.6.3.1

`Fit` N.1.2

Fitting N.1.2, N.1.Sol.14

Fixed points

• of function applications P.3.7, N.1.Ex.15, N.2.Ex.9
• of the logistic map N.1.Ex.1

Fixed-precision

• forcing ~ usage N.1.1.1
• in linear algebra N.1.4

`FixedPoint` P.3.7

`FixedPointList` P.3.7

`Flat` P.3.3

`Flatten` P.6.4.1

`FlattenAt` P.6.4.1

Flattening

• 3D graphics G.2.1.4, G.2.3.4
• of nested lists P.6.4.1

Fleas and dogs N.2.Ex.6

Flexibility, reason of Mathematica's ~ P.2.0

Floating objects, position of ~ P.1.Sol.1

`Floor` N.1.1.3

`FlowerBall` G.3.3

Flowers

• ball of ~ G.3.3
• dodecahedral ~ G.2.Sol.1
• polyhedral ~ P.1.2.2

Flows, branched ~ N.1.Ex.11

Flying

• kite P.1.Sol.1
• saucer G.2.Sol.1

`Fold` P.3.7

Folding

• Christmas stars G.2.3.9
• paper G.2.3.9
• proteins P.1.Sol.1

`FoldList` P.3.7

Foldy-Wouthuysen transformations P.1.Sol.1

`FontColor` G.1.1.1

`FontFamily` G.1.1.1

Fonts

• conventions using various ~ In
• in graphics G.1.1.1

`FontSize` G.1.1.1

`FontSlant` G.1.1.1

`FontWeight` G.1.1.1

`For` P.5.1.4

For all quantifier S.1.2.3

For loop P.5.1.4

`ForAll` S.1.2.3

Force

• -free magnetic fields S.3.Ex.20
• between colliding balls N.1.10.1
• Coriolis ~ S.1.7.1
• Coulomb ~ N.1.10.1
• for a ruler on fingers N.1.Sol.11
• friction ~ N.1.Sol.11
• on a charged particle N.1.Sol.10
• quantum ~ N.1.10.1

Ford circles N.2.Ex.10

Forest fire model P.1.2.1

Form, the computer algebra system P.1.Ex.2

Formatting

• conventions of the GuideBooks In, P.1.1.2
• for brevity P.6.Sol.9, S.1.Sol.17, S.3.Sol.25
• ideal ~ P.6.Ex.16
• in `InputForm` cells In
• inappropriate ~ G.2.3.10
• Mathematica code P.1.1.2, P.6.Ex.16, G.2.3.10
• of arrays P.6.2
• of tables P.6.2
• of too big expressions P.2.3.2
• wrappers P.2.2.1

`FormatType` G.1.1.3, G.2.1.3

Formula

• Abel-Plana ~ S.1.Sol.15
• Boole summation ~ N.2.4
• Campbell-Baker-Hausdorff ~ P.5.Sol.8
• Crofton ~s S.1.9.1
• Darboux-Christoffel ~ S.2.1
• Euler ~ G.1.1.3, N.1.5
• Euler-Maclaurin ~ N.2.4
• Euler-Poincaré ~ G.3.Sol.15
• Euler's ~ G.2.Ex.7
• extended Poisson summation ~ S.1.Sol.15
• Faà di Bruno ~ S.1.Sol.17
• for cos(2pi/17) S.1.9.2
• for cos(2pi/257) S.1.9.2
• for cos(2pi/65537) S.1.9.2
• Frobenius ~ P.6.Ex.18
• Heron's ~ S.1.2.3, S.1.Ex.1
• Jensen's ~ S.1.6.2
• Lagrange-Bürmann ~ S.1.Ex.17
• Larmor's dipole ~ G.2.2.1
• Mehler's ~ S.2.Ex.1
• Meissel ~ for primes P.6.Ex.21
• Meissel's ~ for Bessel functions S.3.Ex.1
• of a trefoil knot S.1.9.3
• operator splitting ~ S.1.Ex.45
• Riemann-Siegel ~ S.3.Ex.15
• Rodrigues's ~ S.2.1
• Schröder's ~ S.1.6.4
• Söddy ~ P.1.2.2, S.1.Ex.1
• Sokhotsky-Plemelj ~ S.1.8
• Stirling's ~ N.2.3
• Waring ~ S.2.Ex.5
• pi-~s N.1.1.1, S.3.Ex.19

FORTRAN

• code generation P.6.Sol.16
• form P.6.Ex.16

Foundations, of Mathematica P.2.0

Fountains, water falling from ~ P.1.Sol.1

Four-color theorem Pr

`Fourier` N.1.5

Fourier

• coefficients P.1.Sol.1
• differentaition N.1.Ex.29

Fourier series

• 2D ~ expansions S.3.5
• and ~ transform S.1.Ex.44
• generalized ~ S.2.1, S.2.Ex.2
• Gibbs phenomena in ~ P.1.2.2, S.2.4
• visualizing the convergence of ~ G.3.1

Fourier transform

• and ~ series S.1.Ex.44
• approximation of the ~ N.1.5
• continuous ~ S.1.8
• discrete ~ N.1.5
• eigenfunctions of the ~ S.1.Ex.44
• for the relativistic oscillator S.2.Sol.7
• fractional ~ N.1.5, S.3.3
• matrix for ~ G.1.Sol.9
• numerical ~ N.1.5
• of data N.1.5
• of discontinuous functions N.1.5
• of greatest common divisors P.1.2.1
• self ~ S.1.8
• symbolic ~ S.1.8
• through Möbius inversion N.2.2
• timings of ~ N.1.5
• uncertainty relation for ~ N.1.5
• used in PDEs N.1.Sol.35

`FourierParameters` N.1.5

`FourierTransform` S.1.8

Fractal

• constructions G.2.3.1, G.3.Ex.8, N.1.3, S.3.5
• curves G.1.2.2
• from iterating Bessel functions S.3.5
• from iterating exp N.1.3
• mountains G.2.Ex.9
• of Newton basins P.3.7, N.1.Ex.15
• post sign P.1.2.2
• tilings G.1.5.5
• tree P.1.2.2

Fractals

• from iterations P.1.2.2
• from power iterations N.1.3
• from solving PDEs N.1.Sol.35
• from Weierstrass iterations N.1.Ex.15
• in 3D G.2.3.1, N.1.Ex.15
• of random functions G.3.Sol.8
• Rauzy ~ G.1.1.1
• triptych ~ G.1.Sol.10
• various 2D ~ G.3.Sol.8

`FractalTree` P.1.2.2

Fractional

• derivative P.1.Sol.1
• differentiation P.1.Sol.1, S.3.Ex.18
• Fourier transform N.1.5
• integration P.1.Sol.1, S.1.Ex.3, S.3.Ex.18
• iteration P.1.Sol.1, S.1.6.4
• part P.2.4.2, N.1.1.3
• part map N.1.Ex.8

`FractionalFourier` N.1.5

`FractionalPart` P.2.4.2

Fractions

• automatically collapsing ~ P.2.2.2
• continued N.1.1.3, N.1.Ex.37, N.2.2
• denominator of ~ P.2.4.1, S.1.3
• Egyptian ~ N.1.1.3
• exact ~ P.2.4.1
• Farey ~ G.1.2.2, N.1.8, N.2.Ex.10
• in the complex plane G.1.1.1
• irreducible ~ P.2.2.2, G.3.Ex.1
• numerator of ~ P.2.4.1, S.1.3
• of all integers N.2.Ex.1
• of expressions S.1.3
• of polynomials S.1.3
• reduced ~ P.2.2.1

`Frame` G.1.1.3

`FrameLabel` G.1.1.3

Frames

• around graphics G.1.1.3
• Frenet ~ G.2.3.2
• interwoven ~ G.2.3.8

`FrameStyle` G.1.1.3

`FrameTicks` G.1.1.3

Franel identity N.1.Ex.3

Fredholm integral equation S.1.Ex.5

`FredholmResolventList` S.1.Sol.5

`FreeQ` P.5.1.2

Frenet frame G.2.3.2

Frequency

• analysis P.6.Ex.1
• estimation N.1.5

Fresnel

• diffraction S.3.3
• functions S.3.3
• integrals S.3.3

`FresnelC` S.3.3

`FresnelS` S.3.3

Freud's weight function S.2.Sol.4

Friction P.1.Sol.1, N.1.Sol.11

Friday the 13th N.2.Ex.7

Friezes, de Bruijn ~ N.2.1

Frisch function N.1.1.3

`FrischF` N.1.1.3

Frobenius formula P.6.Ex.18

Frog model N.1.Ex.27

`FromContinuedFraction` N.1.1.3

`FromDigits` P.2.4.2

`FrontEnd`` P.4.6.6

Frozen, expressions P.3.3

Frullani integral S.1.6.2

`FullDefinition` P.4.4.1

`FullForm` P.2.1

`FullSimplify` S.3.1

`Function` P.3.6

Function

• Ackermann ~ P.4.3.2
• Airy ~ S.3.5
• analytic ~ vanishing for almost all real values P.2.Ex.7
• analytic ~ vanishing for |z|>1 P.2.Ex.7
• analytic ~ vanishing for |z|!=1 P.2.Ex.7
• analytic ~ vanishing outside the unit interval P.2.Ex.7
• anonymous ~ P.3.6
• Appell ~ S.3.7, S.3.Ex.17
• application P.2.2.3
• Belyi ~ G.3.Ex.10, S.3.13
• Bessel ~ S.3.5, S.3.Ex.1
• Beta ~ S.3.2
• binomial ~ N.2.3
• bivariate hypergeometric ~ S.3.7
• Böttcher ~ G.1.1.1
• Brjuno ~ N.1.Ex.37
• Buchstab ~ N.1.10.1
• canonical partition ~ S.3.Ex.12
• Cantor-like ~ N.1.Sol.14
• castle rim ~ P.2.Ex.7
• characteristic ~ S.1.Sol.44
• de Rham's ~ P.1.2.1
• Dedekind eta ~ N.1.Ex.31, S.3.Ex.23
• defined at discrete points only S.3.Ex.11
• Dirac delta ~ S.1.8, S.1.Ex.44, S.3.Ex.12
• Dirichlet ~ P.1.2.2
• error ~ S.3.3
• FAPP-~ S.1.Ex.32
• Fibonacci ~ N.2.4
• Freud's weight ~ S.2.Sol.4
• Frisch ~ N.1.1.3
• Gamma ~ S.3.2, S.3.Ex.1
• generalized exponential ~ S.3.7
• generating ~ S.2.1, S.3.0
• Green's ~ S.1.8, S.3.8, S.3.Ex.8, S.3.Ex.12
• Heaviside ~ S.1.8
• Hurwitz Zeta ~ S.3.Ex.15
• Husimi ~ N.1.Sol.5, S.3.0
• ideal ~ In
• incomplete Beta ~ S.3.2
• incomplete Gamma ~ S.3.2
• introducing a ~ In
• inverse ~ P.2.2.5
• jerk ~ N.1.Ex.34
• Kiesewetter ~ G.2.1.5
• Lambert ~ S.3.10, S.3.Ex.21
• lattice Green's ~ S.1.Ex.31
• Mangoldt ~ N.2.Ex.10
• matrix sign ~ S.1.Ex.2
• Minkowski ~ G.1.2.2, N.1.1.3
• Möbius N.2.2
• Moshinsky ~ S.3.3
• multinomial N.2.3
• polygamma ~ S.1.6.6
• probability distribution ~ S.1.Ex.44
• pure ~ P.3.6
• Ramanujan tau ~ N.2.Ex.14
• random analytic ~ N.1.Sol.2
• rational S.1.Ex.22
• reconstruction from series terms P.1.Sol.1
• Riemann Zeta ~ P.5.Ex.7, S.3.Ex.15
• satisfying no algebraic differential equation S.3.2
• sawtooth ~ P.2.Ex.7
• self-reproducing ~ P.3.6
• shape ~ S.1.Sol.7
• smoothing ~ N.1.Ex.13
• special analytic ~ P.1.Sol.1
• staircase ~ P.2.Ex.7
• step ~ S.1.8
• sum of error ~ N.1.Ex.37
• Tagaki ~ N.1.4
• Takeuchi ~ P.3.5
• totient ~ N.2.2
• Walsh ~ G.1.Ex.12
• Weierstrass ~ G.1.2.2
• Wigner ~ G.2.2.2, S.3.0
• with special inverse S.1.6.4
• Yoccoz ~ S.1.Ex.17
• Zagier's S.3.Ex.11
• zapotchka ~ N.1.Ex.13
• Zeta ~ P.5.Ex.7, S.3.Ex.15
• Zeta Zeta ~ S.3.Ex.15

Function application

• extracting all ~s P.3.4
• infix form of ~ P.2.2.3, P.3.1.3
• input forms of ~ P.3.1.3
• postfix form of ~ P.2.2.3, P.3.1.3
• prefix form of ~ P.3.1.3
• recursive ~ P.3.1.1
• repeated ~ P.3.7

Function definitions

• automatic generation and destruction of ~ P.6.4.4
• automatic generation of ~ P.3.5, N.1.Ex.21
• avoiding certain ~ P.3.4
• clearing ~ P.3.1.2
• complete ~ P.4.4.1
• counting ~ applications P.3.Sol.9, P.5.Sol.8, N.2.Sol.1
• degenerate cases of ~ P.2.2.2, P.6.3.3
• dependencies of ~ P.6.4.2
• for numerical values P.3.4
• for various cases P.3.1.1
• generality of ~ P.3.1.1
• immediate versus delayed ~ P.3.1.2
• indirect generation of ~ P.3.4
• internal form of ~ P.3.4
• mixing delayed and immediate ~ P.3.1.1
• modeling ~ P.5.3.1
• multiple ~ P.3.1.1, P.3.Sol.1
• multiple matching ~ P.3.1.1
• object-oriented ~ P.3.4
• ordering of ~ P.3.1.1
• pitfalls of ~ P.3.1.1
• removing special ~ P.3.1.2
• reordering ~ N.1.Sol.21, S.1.6.2
• simple ~ P.3.1.1
• special numerical ~ P.3.4
• traditionally formatted ~ In, P.1.2.3
• unusual ~ P.3.Ex.1, P.3.Ex.1

Functional

• derivative S.1.Ex.44
• differentiation S.1.Ex.44
• programming constructs P.6.4.3
• programs P.6.Ex.21, G.2.3.10

Functional equation

• de Rham's function P.1.2.1
• of elliptic functions S.3.Ex.4
• of Riemann Zeta function P.5.Ex.7
• of Siamese Sisters curve P.6.5.1
• of Tagaki's function N.1.4
• visualizing solutions of a ~ S.1.Ex.26

Functionals

• differentaiating ~ S.1.Ex.44
• linear ~ S.1.8
• nonlinear ~ N.1.Ex.32

`FunctionDefinitionsTester` P.4.6.5

`FunctionExpand` S.3.1

`FunctionInterpolation` N.1.2

Functions

• 3D plot of ~ G.2.2.1
• adding side effects to ~ S.3.Sol.9
• algebraic ~ S.1.2.3, S.1.5
• aliases of ~ P.4.Ex.3
• all ~ that hold arguments P.3.3
• all ~ with options P.6.4.2
• all built-in ~ P.4.1.1
• application of ~ P.3.1.3
• applied to lists P.3.3
• arctrig ~ P.2.2.5
• arithmetic ~ P.1.2.1
• associative ~ P.3.3
• attributes of ~ P.3.3
• averaging ~ S.2.Ex.9
• bandlimited ~ P.1.Sol.1
• Bessel ~ S.3.5
• Boolean ~ P.5.1.1
• built-in versus user-defined ~ P.3.1.1, N.1.3
• changing heads of ~ P.6.1.1
• combinatorial ~ N.2.3
• commutative ~ P.3.3
• compilable ~ N.1.3
• compiled ~ N.1.3
• conditionally defined ~ P.5.2.2
• continuous but not differentiable P.1.2.2, G.1.2.2
• converting ~ S.1.4
• counting ~ applications P.3.Sol.9, N.2.Sol.1
• counting ~ calls P.6.0, P.6.Ex.25
• decreasing the precision N.1.Sol.23
• defining ~ P.3.1.1
• definitions of ~ P.4.4.1
• derivatives of ~ S.1.6.1
• differentiability of ~ S.1.6.3
• differential algebraic constant ~ P.2.Ex.6, S.1.Sol.22
• differentiating ~ S.1.6.1
• differentiation of ~ P.3.3
• difficult to plot ~ G.1.Ex.14
• direct and inverse ~ P.2.2.5
• disappearing in definitions P.6.Ex.14
• discontinuous ~ in ODEs N.1.10.1
• discussed in this book P.6.Sol.3
• domain of ~ definition P.2.2.3
• doubly periodic ~ S.3.9
• dumped ~ P.6.Sol.19
• easily removable ~ P.3.1.2
• elementary ~ P.2.2.3, S.3.1, S.3.Ex.1
• elliptic ~ P.1.2.3, S.3.0, S.3.9
• ending with `Q` P.5.1.1
• equality of pure ~ P.3.Sol.1
• exponential ~ P.2.2.3
• factorial ~ N.2.3
• failing P.4.1.1
• finding ~ programmatically P.6.Sol.16
• foolable ~ S.1.Ex.32
• fooling built-in ~ G.1.2.1, N.1.7, N.1.Ex.23, N.1.Sol.23
• frequency of the occurrence of ~ P.6.6
• from the standard packages P.4.6.6
• functions of ~ P.3.8
• Gamma ~ S.3.2
• general ~ of matrices P.6.5.3
• generalized ~ S.1.8
• generalized Airy ~ N.1.10.1
• genericity assumptions about ~ S.1.8
• Hankel ~ S.3.Ex.13
• higher order ~ P.3.8
• higher special ~ S.3.1
• hyperbolic ~ P.2.2.3
• hyperelliptic ~ N.1.11.2
• hypergeometric ~ S.3.13
• hypergeometric type ~ S.3.7
• hyperspherical ~ S.2.Ex.6
• increasing the precision N.1.Sol.23
• integrating ~ S.1.6.2
• inverse ~ P.1.Sol.1, P.3.8, N.1.Sol.23, S.1.5, S.3.Ex.3
• inverse hyperbolic ~ P.2.2.5
• inverse trigonometric ~ P.2.2.5
• invertible by Mathematica P.3.8
• investigating all system ~ P.6.4.2
• iterated ~ P.2.Ex.9, G.1.5.6
• iteration of ~ P.3.7, G.1.2.1, N.1.Ex.1
• Lambert ~ S.3.10
• Legendre ~ S.3.6, S.3.Ex.14
• listing all built-in ~ P.4.1.1
• logarithmic ~ P.2.2.3
• mapping ~ directed P.6.3.3
• mapping ~ everywhere P.6.3.3
• mapping ~ over lists P.6.3.3
• Mathieu ~ S.3.11
• matrix ~ S.1.Ex.2
• Meijer G ~ S.3.7
• multivalued ~ P.2.Ex.6, G.2.3.7, G.3.3, N.1.11.2, S.1.6.2, S.1.Ex.23, S.3.10, S.3.Ex.3, S.3.Ex.16, S.3.Ex.21
• multivariate ~ P.1.Sol.1, P.3.1.1, S.3.7
• names of all Mathematica ~ P.4.1.1
• naming conventions for ~ P.1.1.1
• nonsmooth ~ G.1.Ex.14
• nowhere differentiable ~ P.1.2.2, G.1.2.2, G.1.3.1
• number of built-in ~ P.4.1.1
• number-theoretic ~ N.2.2
• numeric ~ P.3.3, P.5.1.1
• obsolete ~ P.4.1.1, P.6.Sol.19
• of linear algebra P.6.5.1
• of matrices P.6.5.3, N.1.7
• options of ~ P.3.2
• patterns in ~ definitions P.3.1.1
• piecewise-defined ~ P.5.1.4, G.2.3.4, S.1.8
• plotting ~ G.1.2.1
• polygamma ~ S.3.2
• productlog ~ S.3.10
• protected ~ P.6.4.2
• Ramanujan theta ~ S.3.0
• random ~ G.2.Sol.18, G.3.Sol.8, S.1.Ex.16
• random rational ~ N.1.3
• rational ~ S.1.3
• recursive definitions of ~ P.4.4.1
• related to accuracy and precision N.1.1.1
• repeated application of ~ P.3.7
• returning `True` or `False` P.5.1.1
• returning unevaluated for inappropriate arguments P.5.2.2
• scoping in ~ with iterators P.4.6.1
• searching for interesting ~ G.3.Sol.8, N.1.Sol.34
• separability of ~ P.5.Ex.15
• setting attributes of ~ P.3.3
• setting options of ~ P.3.2
• special ~ S.3.0
• spherical Bessel ~ S.3.5
• system ~ as strings P.6.4.2
• testing ~ P.5.1.1
• that compile automatically N.1.1.5
• that generate functions P.3.6
• that remember their values P.3.5
• that return numbers P.3.3
• that take level specifications P.5.1.4, P.5.2.2, P.6.4
• theta ~ S.3.0, S.3.Ex.12
• threading ~ over arguments P.6.4.3
• to be treated especially P.4.Sol.4
• top ten used ~ P.6.6
• trigonometric ~ P.2.2.3, S.1.4
• undocumented ~ P.4.1.1, N.2.3
• unprotected built-in ~ P.3.1.2
• unusual analytic ~ P.2.Ex.7
• usage messages of numeric ~ S.3.Ex.9
• used too early P.6.Ex.4
• user-defined factorial ~ P.1.2.4
• user-defined Fibonacci ~ N.2.4
• visualization of inverse ~ G.2.Sol.21, S.3.Sol.3
• Wannier ~ S.3.11
• with attributes P.6.4.2
• with boundary of analyticity G.3.Ex.16, N.1.10.1, N.1.Ex.2, N.2.Sol.10
• with certain attributes P.6.4.2
• with level specifications P.6.Ex.16
• with long names P.6.4.2
• with many arguments P.3.1.1
• with many attributes P.6.4.2
• with many options P.3.2
• with options P.5.3.1, P.6.4.2
• with palindromic names P.6.4.2
• with short names P.6.4.2
• with values P.4.Sol.4

Fundamental

• domain S.1.3
• solution of differential equations S.1.8, S.3.8, S.3.Ex.8, S.3.Ex.12
• theorem of algebra P.1.2.1
• theorem of calculus S.1.6.2
• theorem of number theory N.2.1

## G

Gaits modeling P.1.Sol.1

Gale-Robinson sequence S.1.3

Galilei invariance P.1.Sol.1, S.1.Ex.29

Galois theory S.1.5

Galton board N.2.Ex.6

`GaltonBoard` N.2.Sol.6

Game

• house of the Nikolaus ~ P.5.3.3
• monopoly ~ P.1.Sol.1
• of life G.1.Ex.1, N.1.Sol.32
• preparing for a card ~ N.2.Ex.6
• Scrabble ~ P.6.4.4
• Sorry ~ P.5.2.2
• swing jumping ~ S.1.Ex.10

`Gamma` S.3.2

Gamma function

• asymptotics of ratio of ~s S.3.Ex.1
• asymptotics of the ~ S.3.Ex.1
• definition of the ~ S.3.2
• fast integer evaluation of ~ P.1.2.4
• identities S.3.Ex.25
• Riemann surface of the incomplete ~ S.3.2
• visualization of the ~ S.3.Ex.1

Gamma matrices P.5.2.1, P.6.Ex.9

Gamov states S.3.Ex.10

Gases in equilibrium P.1.Sol.1, N.1.Ex.12

Gauge

• Landau ~ N.1.8
• transformation for a square S.3.Ex.20

Gauss

• C. F. N.2.2, S.1.9.2
• curvature G.3.Ex.15, S.1.6.1
• distribution N.1.Ex.25, N.1.Sol.25
• map P.1.2.2, P.3.7
• periods S.1.9.2
• prime counting approximation N.2.2
• reciprocity law N.2.2
• sums G.3.2

Gauss-Bonnet theorem G.3.Ex.15

Gauss-Kusmin distribution N.1.1.3

Gauss-Lucas theorem S.3.Ex.18

`GaussCurvature` G.3.Sol.15

Gaussian

• integers G.1.1.2, N.2.1
• polynomials S.1.Ex.30
• primes P.5.1.1, G.3.2

`GaussKronrod` N.1.7

`GaussPoints` N.1.7

Gayley, T. P.6.Sol.19

`GCD` N.2.1

Gcd-free partitions S.1.Ex.30

Gcd-lcm iterations N.2.Ex.14

`GCDFreePartition` S.1.Sol.30

`GCDFreePartitions` S.1.Sol.30

`GCDSteps` N.2.Sol.1

`Gear` N.1.10.1

Gear

• chain animation G.2.Ex.19
• teeth P.1.Sol.1

Gear method, for solving ODEs N.1.10.1, N.1.Sol.16

Gegenbauer polynomials

• definition of ~ S.2.4
• in Gibbs phenomena-free Fourier series S.2.4
• in multidimensional expansions S.2.4, S.2.Ex.6
• in multipole expansions S.2.Ex.6

`GegenbauerC` S.2.4

Genealogical tree P.1.Sol.1

`General` P.4.1.1

General

• definitions P.3.1.1
• information about Mathematica P.1.1.1, A.1.3
• messages P.4.1.1
• orthogonal polynomials S.2.Ex.4
• overview P.1.0

Generality, of patterns P.3.1.1

Generalized

• Airy functions N.1.10.1
• Clebsch surface S.1.Ex.27
• cross product P.6.4.3
• ellipse S.1.Ex.28
• error function S.3.7
• expansions N.1.1.3
• Fourier expansion S.2.1
• Fourier series S.2.Ex.2
• functions S.1.8
• hypergeometric function S.3.7
• Lissajous figures S.2.Ex.6
• Maurer roses N.2.1
• multinomial theorem N.2.Ex.14
• Pythagoras theorem G.1.1.1
• residue S.1.6.5
• scalar product P.6.4.3
• solutions of differential equations S.1.8
• table P.6.Sol.8
• Taylor expansion S.1.6.1
• trigonometric functions N.1.Ex.2
• Weierstrass function P.1.2.2

`GeneralizedFourierCoefficient` S.2.Sol.2

`GeneralizedFourierSum` S.2.Sol.2

`GeneralizedHyperbolicPlato` G.2.3.10

`GeneralizedLissajousFigure` S.2.Sol.6

`GeneralizedMaurerRose` N.2.1

`GeneralizedTaylorSeries` S.1.6.1

`GeneralOrthogonalPolynomials` S.2.Sol.4

`GenerateConditions` S.1.6.2

Generating function

• of associated Legendre polynomials S.2.6
• of first kind Chebyshev polynomials S.2.7
• of Gegenbauer polynomials S.2.4
• of harmonic numbers S.3.0
• of Hermite polynomials S.2.2
• of Jacobi polynomials S.2.3
• of Laguerre polynomials S.2.5
• of Legendre polynomials S.2.6
• of orthogonal polynomials S.2.1
• of second kind Chebyshev polynomials S.2.8

Generation

• of compiled code N.1.3
• of conditions in integration S.1.6.2
• of evaluation outlines P.4.5
• of fractals G.3.Ex.8
• of function definitions P.3.5, N.1.Ex.21
• of identities in divisor sums N.2.Ex.10
• of identities in Gamma functions S.3.Ex.25
• of identities in harmonic numbers S.3.0
• of jerk functions N.1.Ex.34
• of modular equations S.3.Sol.25
• of normal distributed random numbers N.1.Sol.25
• of optimized code N.1.11.1
• of random expressions G.1.5.6, G.1.Ex.16
• of random functions S.1.Ex.16
• of random IFSs G.1.5.6
• of random L-systems G.1.5.9
• of random polyhedra G.2.Sol.1, G.2.Sol.18
• of solvable evolution equations S.3.Sol.4
• of specialized function definitions N.1.Ex.21
• of strange attractors N.1.Ex.9
• of subsets P.6.Ex.6

Generic

• cases P.6.0
• intersections S.1.Ex.39
• solutions S.1.5

Genericity assumptions S.1.1, S.1.8

Genetic code P.1.Sol.1

Genus, k surfaces G.2.Ex.7

`Geode` G.2.2.1

Geodesics S.1.6.1, S.3.8

Geometric

• mean S.1.2.3
• mean of irreducible fractions S.3.Ex.1
• theorem proving P.1.2.3, S.1.2.2, S.1.Ex.1, S.1.Sol.1

Geometry packages P.4.6.6

`Get` P.4.4.1

GHZ state S.1.2.3, S.1.Ex.21

Gibbs

• distribution N.1.Ex.25
• phenomena P.1.2.2, N.1.Ex.22, S.2.4

Ginzburg-Landau, complex ~ equation N.1.10.2

`Glaisher` N.1.Ex.14

Global

• relative acttractors N.1.1.2
• variables P.4.6.4

`Global`` P.4.6.4

`Global`Trace` P.6.5.1

`GlobalWeierstrassIterations` N.1.Sol.15

Glued strip, graphic of a ~ G.2.Ex.10

`GluedPolygons` P.6.0

`GluedPolygonsAnalysis` P.6.Ex.25

Gluing, surfaces together G.3.3

Goals, of the GuideBooks Pr

Gödel, K. P.4.0

Goffinet

• dragon N.1.Sol.32
• graphic of a charged ~ dragon G.3.1
• kite G.2.3.9
• points of a ~ dragon G.1.1.1

`GoffinetPicture` G.1.1.1

Goldbach problem N.2.Ex.12

Golden ratio P.2.2.4

`GoldenRatio` P.2.2.4, N.1.Ex.20

`Gosper` G.1.5.9

Gosper

• curve G.1.5.9, N.1.5
• W. N.1.5

Gotha (in Thuringia) P.6.4.4, N.2.Sol.2

Gothic letters P.1.1.2

`Goto` P.4.6.2

`Gradient` N.1.9

• curves N.1.Ex.10
• method N.1.9

Graeffe method S.1.Ex.6

Gram-Schmidt orthogonalization S.2.Ex.4

`GramDet` P.6.Sol.18

Grammar, learning ~ P.1.Sol.1

Graphic

• aircraft-like ~ G.2.Sol.1
• of a birthday bow G.2.2.1
• of a butterfly G.3.1
• of a candelabra G.2.2.1, G.3.3
• of a chicken wire G.2.2.1
• of a Clebsch surface N.1.Ex.7
• of a colored strip G.2.2.1
• of a cube-rooted sphere S.1.Ex.37
• of a cubed sphere S.1.Ex.37
• of a dodecahedron G.2.1.5
• of a glue strip G.2.Ex.10
• of a Goffinet dragon G.3.1
• of a heart G.3.1
• of a scale G.2.1.5
• of a screw G.2.Sol.1
• of a shaft G.2.2.1
• of a Sierpinski plant G.2.Ex.22
• of a snail G.2.Ex.4
• of a spindle S.1.Ex.37
• of a torus G.2.1.5
• of a vase G.2.Sol.1
• of a witch house G.2.2.1
• of an arrow G.2.2.1
• of an impossible crate G.2.3.6
• of an octopus G.2.Sol.1
• of Berger's maple leaf G.1.5.6
• of Borromay rings G.2.2.1
• of bricks G.2.Sol.1
• of broken tubes G.2.Sol.1
• of Easter eggs G.2.3.3
• of plies G.2.Sol.1
• of the earth G.3.2
• of the yin-yang G.1.1.1
• of worn stones G.2.Sol.1

Graphic options G.1.1.3, G.2.1.3 Graphica G.1.0

`Graphics` G.1.1.1

Graphics

• adding randomness to ~ G.1.5.6, G.2.Sol.18
• animating ~ G.1.3.2
• arrays of ~ G.1.3.1
• arrows in ~ G.1.4
• as expressions P.3.2
• as PostScript G.1.1.3
• aspectratio of ~ G.1.1.3, G.2.1.3
• avoiding the display of ~ G.1.3.1
• axes in 2D ~ G.1.1.3
• axes in 3D ~ G.2.1.3
• background of ~ G.1.1.3, G.2.1.3
• Barbé ~ G.3.Ex.5
• boxing of ~ G.2.1.3
• build from primitives G.2.1.2
• colors in ~ G.1.1.2
• combining ~ G.1.3.1, G.3.2, S.3.Sol.1
• comparing options of ~ functions G.3.1
• comparing various ~ G.3.0
• connecting shapes in different ~ S.1.Sol.13
• containing randomness G.1.5.6
• contour ~ G.3.1
• contour lines in 3D ~ G.3.Ex.13
• conversion G.2.2.1
• converting 3D ~ G.2.1.4
• converting 3D ~ to 2D ~ G.2.1.4
• converting contour ~ G.3.1
• converting density ~ G.3.2
• converting surface ~ G.2.2.1
• coordinate systems in 2D ~ G.1.1.1
• coordinate systems in 3D ~ G.2.1.3
• cover ~ In
• cuboids in ~ G.2.1.1
• defaults in ~ G.1.1.3
• directives G.1.1.2
• display of ~ G.1.1.3, G.2.1.3
• displaying ~ G.1.1.1
• Escher-type ~ G.1.5.8
• facegrids in 3D ~ G.2.1.3
• fonts in ~ G.1.1.3
• frames around ~ G.1.1.3
• from ~ to animations G.1.1.1
• from plots and from scratch G.2.3.0
• illumination in 3D ~ G.2.1.1, G.2.1.3
• in 2D G.1.0
• in 3D G.2.1.1
• in 4D G.2.3.0
• in teaching G.1.0
• inversion of ~ G.1.1.1, G.1.5.2, G.1.5.5, G.2.1.5
• iterative 2D ~ G.1.5
• iterative 3D ~ G.2.3.1
• kaleidoscope ~ G.1.5.6
• labels of ~ G.1.1.3, G.2.1.3
• light sources in 3D ~ G.2.1.3
• lightening in 3D ~ G.2.1.3
• long-range correlations in ~ code N.1.1.5
• made from ~ primitives G.1.5.0
• mapping ~ into polygons G.1.5.4
• mixing various types of ~ G.3.2
• objects G.1.1.1
• of Airy functions S.3.5
• of As in 3D G.2.1.2
• of Bessel functions S.3.5
• of double tori G.2.Ex.2, G.3.Ex.15
• of elliptic functions S.3.9
• of elliptic integrals S.3.8
• of equipotential lines G.3.1
• of equipotential surfaces G.3.3
• of error functions S.3.3
• of exponential integrals S.3.4
• of field lines N.1.11.1
• of first kind Chebyshev polynomials S.2.7
• of Gamma functions S.3.2
• of Gegenbauer polynomials S.2.4
• of Hermite polynomials S.2.2
• of hyperbolic Platonic solids G.2.3.10
• of impossible objects G.2.3.6
• of interwoven frames G.2.3.8
• of Jacobi polynomials S.2.3
• of Klein bottles G.2.3.4
• of L-systems G.1.5.9
• of Laguerre polynomials S.2.5
• of Legendre functions S.3.6
• of Legendre polynomials S.2.6
• of lizards G.1.5.8
• of Mathieu functions S.3.11
• of mod N.2.1
• of Pochhammer symbols S.3.2
• of polyhedra G.2.1.5
• of polyhedral flowers P.1.2.2
• of polynomial roots P.1.2.1
• of product log functions S.3.10
• of Riemann surfaces G.2.3.7, N.1.11.2
• of second kind Chebyshev polynomials S.2.8
• of triple tori G.2.Ex.2, G.3.Ex.15
• of vortices G.3.1
• operations on ~ G.1.3.1
• packages P.4.6.6
• perspective in 3D ~ G.1.1.1, G.2.3.6, G.2.Ex.15
• photomosaics made from ~ G.3.2
• primitives G.1.1.1, G.2.1.1
• random ~ G.2.3.1, G.2.Ex.1, G.2.Ex.16, G.3.3
• rotated labels in ~ G.1.1.3
• Saunders ~ G.3.2
• self-similar ~ G.1.1.1, G.1.5
• showing ~ G.1.1.1
• size of ~ G.1.1.3, G.2.1.3
• tall ~ G.1.1.3, G.2.1.5
• textstyles in ~ G.1.1.1
• ticks in ~ G.1.1.3, G.2.1.3
• type of surfaces G.2.2.1
• using symmetries in ~ G.2.4, G.3.Ex.9, G.3.Ex.9, N.1.Sol.19
• various 2D ~ G.1.1.1
• various 3D ~ G.2.Sol.1
• viewpoint in 3D~ G.2.1.3
• with legends P.6.Sol.1
• with symmetry of a cube G.2.Sol.1

`Graphics`Colors`AllColors` G.1.1.2

`Graphics`ContourPlot3D`` P.6.4.2, G.3.Ex.18

`Graphics`ImplicitPlot` G.1.4

`Graphics`Legend`` P.6.Sol.1

`Graphics`ListContourPlot3D` G.3.3

`Graphics`PlotField`` G.1.4, S.3.Sol.2

`Graphics`Polyhedra`` G.2.1.5

`Graphics`Polyhedra`OpenTruncate` G.2.1.5

`Graphics`Polyhedra`Stellate` G.2.1.5

`Graphics`Polyhedra`Truncate` G.2.1.5

`Graphics`Shapes`` G.2.1.5

`Graphics3D` G.2.1.1

`Graphics3D`BarChart3D` G.2.2.2

`GraphicsArray` G.1.3.1

`GraphicsSpacing` G.1.3.1

Grasses and herbs G.1.5.9

Gravitational potential

• in the three-body problem N.1.10.1
• of polyhedra P.1.Sol.1

Gray level specification G.1.1.2

`GrayLevel` G.1.1.2

`GrayRhombusesPartition` P.1.1.2

`Greater` P.5.1.1

`GreaterEqual` P.5.1.1

Greatest common divisor P.1.2.1, N.2.1

Greechie diagrams P.1.Sol.1

Greek letters

• in inputs P.1.1.2
• problem suggestions P.1.Sol.1

Green's function S.1.8, S.3.3, S.3.8, S.3.Ex.12

Greenberger-Horne-Zeilinger state S.1.2.3, S.1.Ex.21

Greuel, G.-M. P.1.3

Grid

• distorted ~ G.1.1.1
• on top of a graphic G.1.1.3
• superimposed ~ G.1.1.1
• superimposing ~s G.1.3.2

`GridLines` G.1.1.3

Grignani

• F. G.1.Sol.8
• pattern G.1.Sol.8

Gröbner basis

• applications of ~ S.1.2.2
• calculation of ~ S.1.2.2
• conversion S.1.2.2, S.1.Sol.25
• showing inconsistency of equations using ~ S.1.2.2
• used for bringing equations to pseudotriangular form S.1.2.2
• used for elimination of variables S.1.2.2
• used for equation solving S.1.2.2
• used for simplifications S.3.9
• with inexact coefficients S.1.2.2

Gröbner walk S.1.2.2, S.1.Sol.25

`GroebnerBasis` S.1.2.2

`GroebnerBasis` in action P.1.2.3, G.1.2.1, S.1.2.2, S.1.Sol.1, S.1.Sol.37, S.3.Sol.3, S.3.Sol.3

Ground state

• high-precision value for the quartic oscillator ~ N.1.Ex.24, S.2.10
• in 2D potentials N.1.4, S.3.5, S.3.11
• in a random 1D potential N.1.Sol.5
• zero energy ~ S.3.Ex.1

Grouping, of numbers P.6.Ex.12

Groups

• behavior of ~ N.1.Ex.27
• generated by pure functions P.6.Ex.8
• hexahedral ~ G.3.Ex.9
• icosahedral ~ G.3.Ex.9
• numerically generated from generators N.1.Ex.37
• of identical elements P.6.3.3, P.6.Sol.12
• of the genetic code P.1.Sol.1
• tetrahedral ~ P.6.Sol.8
• using symmetry ~ in graphics G.3.Ex.9
• visualizing multiplication tables of ~ G.3.2

Growth

• of icicles P.1.Sol.1
• of lists P.6.1.1
• of random clusters N.1.Ex.32
• of snowflakes P.1.Sol.1
• processes G.1.Ex.1

Guard digits

• concept of ~ N.1.1.1
• exposing ~ N.1.1.1, N.1.Ex.23

Guessing

• a sum S.1.Ex.1
• ODE solutions S.1.Sol.1
• sequences S.2.Sol.3

Guiasu, prime counting approximation N.2.2

`GuiasuPrimePi` N.2.Sol.10 GuideBooks

• analyzing the ~ by program P.6.6
• chapter structure of the ~ In
• consistency of references of the ~ P.6.Ex.4
• data about the ~ In
• development of the ~ Pr
• disclaimer of the ~ Pr
• electronic components of the ~ Pr, In
• exerices and solutions of the ~ In
• formatting of the ~ In
• goals of the ~ Pr
• Graphics volume of the ~ Pr
• history of the ~ Pr, In
• homepage of the ~ Pr
• index creation for the ~ In, P.6.Ex.3
• level of the ~ Pr
• Mathematica code in the ~ In
• notations used in the ~ In
• Numerics volume of the ~ Pr
• outline of the ~ In
• overview of the ~ In
• overviews in the ~ Pr, In
• Programming volume of the ~ Pr
• references of the ~ In
• remarks in the ~ In
• resources needed for the ~ In
• statistics of the ~ P.6.6
• Symbolics volume of the ~ Pr
• units used in the ~ In
• Gumbel distribution S.3.Ex.1

Gutzwiller-Maslov theory P.1.2.1

## H

• integrals S.1.8
• integration ~ S.1.6.2
• matrices S.1.Ex.1
• prime counting approximation N.2.2

Half-periods S.3.Sol.3

Halley map G.3.Sol.8

`HalleyChebyshevMap` G.3.Sol.8

`HalleyMap` G.3.Sol.8

Hamilton-Jacobi equation

• classical ~ S.1.7.2
• quantum ~ N.1.10.1

Hamiltonian

• anharmonic oscillator ~ S.2.10
• Calogero-Sutherland ~ S.2.9
• Kohmoto ~ N.1.8

Hamlet N.1.1.5

Hand, optimal ~ P.1.Sol.1

Hankel

• determinant N.2.4
• functions S.3.Ex.13

`HankelDet` N.2.4

Hannay angle N.1.Ex.4

Hansen-Patrick method N.1.3

Harmonic

• numbers P.1.2.1, S.3.0
• polylogarithms S.3.Ex.15

Harmonic oscillator

• 3D ~ S.3.Ex.12
• damped ~ S.1.Ex.19
• eigenvalues of the ~ S.3.Ex.5
• FEM treatment of the ~ S.1.Ex.7
• inverted ~ N.1.Sol.5, S.3.7
• multidimensional ~ S.2.Ex.9
• nonlinear ~ N.1.Ex.4
• optimized ~ expansion N.1.Ex.5
• perturbed ~ S.2.Ex.10
• shifted ~ S.2.2
• time-development of ~ S.3.3
• uniform approximation of the ~ S.3.5

Harmonics

• hyperspherical ~ S.2.Ex.6
• spherical ~ S.2.Ex.1

Harper equation N.1.8

`Hash` P.6.Ex.24

Hash values P.6.Ex.24

`Head` P.2.1

`Heads` P.2.3.2

• and arguments P.2.1
• as a level specification P.2.3.2
• changing ~ of expressions P.6.1.1
• compound ~ P.2.1
• exchanging ~ and arguments P.6.3.3
• extracting ~ P.3.1.1
• faked ~ P.3.Ex.5, N.1.Sol.23
• function definitions for compound ~ P.3.4
• numerical ~ P.3.3
• of exact numbers P.2.2.1
• of expressions P.2.1
• of inexact numbers P.2.2.1
• prescribed in patterns P.3.1.1
• with arguments P.2.1
• with attributes P.3.3
• with hold attributes P.3.3

Heart, graphic of an algebraic ~ G.3.1

Heat

• conduction P.1.Sol.1
• engine P.1.Sol.1
• equation S.3.Ex.12
• specific ~ S.3.Ex.12

Heaviside function S.1.8

Hedgehog G.1.2.1, S.1.Ex.25

Heegner numbers N.1.Sol.31

Heilbronn triangle problem S.1.9.1

Heisenberg uncertainty relation N.1.5

Held

• arguments P.3.3
• patterns P.5.2.1

`HeldPart` P.3.3

Helicopter noise P.1.Sol.1

Helium atom S.1.Ex.8

Hellmann-Feynman theorem N.1.Sol.5

Helmholtz

• coil S.3.Ex.2
• equation N.1.2, S.3.5
• operator N.1.Ex.16
• random ~ equation solutions S.3.Ex.13

Help browser P.1.2.1

Henneberg surface G.2.Sol.1, S.1.6.2

Hénon map N.1.Ex.9

Heptagons, forming polyhedra P.6.0

Hermite polynomials P.5.Ex.10, S.1.Sol.44, S.2.2, S.2.10

`HermiteH` S.2.2

`HermiteLaguerreRelation` S.2.9

`HermiteZeroMoment` S.2.Sol.7

Heron's formula S.1.2.3, S.1.Ex.1

Hershey text G.1.1.3, G.2.1.2

Hessian S.3.13

Hexagon

• -triangle transition G.2.1.5
• largest ~ of unit diameter S.1.2.2
• subdivision of a ~ G.1.1.1

Hexagons

• in 3D contour plots G.3.Ex.19
• lizards in ~ G.1.5.8
• on a torus G.2.Ex.2
• on knots G.2.3.2
• polyhedra made from ~ P.6.0

Hidden

• derivative definitions S.3.Ex.9
• edges G.2.Ex.15
• polygons G.2.1.5
• variables N.1.10.1, S.1.2.3
• zeros N.1.Sol.23

`HiddenSurface` G.2.2.1

High-order

• Brillouin zones G.1.Sol.2
• perturbation theory S.1.7.1, S.1.8, S.2.Ex.10

High-precision

• automatic ~ comparisons P.5.1.1
• automatic switch to ~ arithmetic N.1.1.1
• checking of identities N.1.0, N.1.Ex.2, S.3.0, S.3.Sol.25
• evaluations for special functions S.3.Ex.9
• integration N.1.Ex.14
• linear algebra N.1.4
• logistic map iterations P.1.2.1, N.1.1.1
• solution of ODEs N.1.Sol.3
• value for the quartic oscillator ground state N.1.Ex.24, S.2.10
• values of pi N.1.Ex.8

High-precision arithmetic

• in action P.1.2.1, N.1.0, N.1.4, N.1.Ex.8, N.1.Ex.24, S.2.10
• in equality testing P.5.1.1
• in iterator calculations P.4.2.1
• in symbolic computations S.1.2.2
• modeling ~ N.1.1.1, N.1.Ex.20
• principles of ~ P.1.2.1, P.2.2.7
• versus machine arithmetic N.1.0

High-precision numbers

• accuracy of ~ N.1.1.1
• analyzing ~ N.1.1.1
• arithmetic with ~ N.1.1.1
• inputting ~ P.2.2.1, P.2.2.7
• large ~ N.1.1.1
• manipulating ~ N.1.1.1
• normalizing ~ N.1.1.1
• occurrences of ~ N.1.1.1
• precision of ~ N.1.1.1
• versus machine numbers N.1.1.0

Higher-order

• ODEs N.1.10.1, S.1.7.1
• root finding algorithms S.1.6.4

Hilbert

• curve in 3D P.1.2.4
• D. P.1.Sol.2
• matrix P.1.2.1, P.6.5.1
• space formulation of classical mechanics P.1.Sol.1
• transform G.2.2.1

`HilbertCurve3D` P.1.2.4

Hill determinant S.2.10

History

• of a session P.4.3.2
• production ~ In

Hölder

• summation S.1.6.6
• theorem S.1.5

Hörselgau (in Thuringia) P.6.5.2

• butterfly N.1.8
• D. N.1.8

`HofstadterButterfly` N.1.8

`Hold` P.3.3

`HoldAll` P.3.3

`HoldAllComplete` P.3.3

`HoldFirst` P.3.3

`HoldForm` P.3.3

`HoldPattern` P.4.1.1, P.5.2.1

`HoldRest` P.3.3

Homogeneous

• differential equations S.1.7.1
• distribution of contour lines G.3.1, N.1.Sol.10, N.2.Sol.10, S.2.10, S.3.2, S.3.6

Homotopy method N.1.10.1, N.1.Sol.1, S.2.Sol.7, S.3.Sol.15

Honeycomb arrays G.1.5.8

Horned sphere G.2.Ex.13

Horner form, of polynomials S.1.Ex.2

Horse, modeling ~ gaits P.1.Sol.1

Hourglass P.1.Sol.1

House of the Nikolaus P.5.3.3

`Hue` G.1.1.2

Hue color specification G.1.1.2, G.1.1.2

Hurwitz

• problem P.1.Sol.1
• Zeta function S.3.Ex.15

Husimi function N.1.Sol.5, S.3.0

Huygen's principle P.1.Sol.1

Hydra, fighting a ~ P.1.Sol.1

Hydrogen, orbitals P.1.Sol.1, S.2.Ex.6

Hylleraas-Undheim helium calculation S.1.Ex.8

Hyperbolic

• cube P.1.2.2, G.2.3.10
• dodecahedron G.2.3.10, G.2.3.10
• functions P.2.2.3
• game of life G.1.Sol.1
• icosahedron G.2.3.10
• octahedron G.2.3.10
• PDEs N.1.10.2, N.1.Ex.36, N.1.Sol.36
• Platonic solids G.2.3.10
• tessellation of the ~ plane G.1.5.8
• tetrahedron G.2.3.10
• triangles G.1.5.8

`HyperbolicDodecahedron` G.2.3.10

`HyperbolicPlato` G.2.3.10

`HyperbolicPlatonicSolid` G.2.3.10

`HyperbolicTriangle` G.1.5.8

Hypercube N.1.Sol.13

Hyperelliptic

• curve G.3.Ex.11
• function N.1.11.2

Hypergeometric

• differential equations S.1.8
• representation of associatedLegendre polynomials S.2.6
• representation of first kind Chebyshev polynomials S.2.7
• representation of Gegenbauer polynomials S.2.4
• representation of Hermite polynomials S.2.2
• representation of Jacobi polynomials S.2.3
• representation of Laguerre polynomials S.2.5
• representation of Legendre polynomials S.2.6
• representation of second kind Chebyshev polynomials S.2.8
• sums S.1.6.6

Hypergeometric functions

• applications of ~ S.3.7
• as solutions of polynomial equations S.3.13
• bivariate ~ S.3.7
• confluent ~ S.3.7
• contiguous relations for ~ S.3.7
• definitions of ~ S.3.7
• differential equation for ~ S.3.7
• Gauss ~ S.3.7
• generalizations of ~ S.3.7
• generalized ~ S.3.7
• Kummer relations for ~ S.3.Sol.17
• references to ~ S.3.7
• regularized ~ S.3.7
• Riemann surfaces of ~ S.3.Sol.16

`Hypergeometric1F1` S.3.7

`Hypergeometric2F1` S.3.7

`Hypergeometric2F1Regularized` S.3.7

`HypergeometricPFQ` S.3.7

`HypergeometricU` S.3.7

Hyperspherical

• coordinates S.1.Ex.9, S.2.4
• harmonics S.2.Ex.6

Hypocycloidal torus G.2.3.5

Hypothesis, Riemann ~ P.5.Sol.7