Index of the GuideBooks

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

• Chladny ~ G.3.Ex.3
• 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
• references about ~ G.3.Sol.8
• 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 compound heads P.3.4
• 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 new special S.3.0
• 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
• overloading ~ P.6.5.1
• 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

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
• paradoxical ~ P.1.Sol.1
• 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
• linking number N.1.7
• map P.1.2.2, P.3.7
• periods S.1.9.2
• prime counting approximation N.2.2
• quadrature rule N.1.7
• 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

Gradient

• 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

Hadamard

• 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

Heads

• 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

Hofstadter

• 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