Index H
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Haar measure
§35.4(i)
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Hadamard’s inequality for determinants
§1.3(i)
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Hahn class orthogonal polynomials
§18.19—§18.24
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Hahn polynomials, see Hahn class orthogonal polynomials.
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Hamiltonian systems
-
handle
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Hankel functions
§10.1
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Hankel transform
§10.22(v)
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Hankel’s expansions
-
Hankel’s integrals
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Bessel functions and Hankel functions
§10.9(iv)
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Hankel’s inversion theorem
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Hankel’s loop integral
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harmonic analysis
-
harmonic functions
§1.9(ii)
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harmonic mean §1.2(iv), §1.7(iii)
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harmonic oscillators
-
harmonic trapping potentials
-
parabolic cylinder functions
§12.17
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heat conduction in liquids
-
heat theory
-
Heaviside function §1.16(iv), §2.6(iii)
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Heine’s formula
-
Heine’s integral
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Helmholtz equation
-
Herglotz generating function
§14.30(ii)
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Hermite polynomials §18.3, see also classical orthogonal polynomials.
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addition theorem
§18.18(ii)
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applications
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asymptotic approximations
§18.15(v)
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computation
Ch.18
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continued fractions
§18.13
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definitions
Table 18.3.1
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derivatives
§18.9(iii)
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differential equations
Table 18.8.1
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Dirac delta
§1.17(iii)
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expansions in series of §18.18(iii), §18.18(iv), §18.18(v), §18.18(vii), §18.18(viii), §18.18(i), §18.18(ii)
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explicit representations
§18.5—§18.5(iv)
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Fourier transforms
§18.17(v)
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generating functions
§18.12
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graphs Figure 18.4.7, Figure 18.4.7, Figure 18.4.7
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inequalities §18.14(iii), §18.14(i), §18.14(ii)
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integral representations §18.10(ii), §18.10(iv), Table 18.10.1
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integrals §18.17(ix), §18.17(vi), §18.17(viii), §18.17(i), §18.17(iii)
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interrelations with other orthogonal polynomials Figure 18.21.1, Figure 18.21.1, Figure 18.21.1, §18.21(ii), §18.7—§18.7(iii)
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Laplace transform
§18.17(vi)
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leading coefficients
Table 18.3.1
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limiting forms as trigonometric functions
§18.11(ii)
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linearization formulas
§18.18(v)
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local maxima and minima
§18.14(iii)
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Mellin transform
§18.17(vii)
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monic Figure 18.4.7, Figure 18.4.7, Figure 18.4.7, §3.5(v)
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multiplication theorem
§18.18(iii)
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normalizations
Table 18.3.1
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notation
§18.1(ii)
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orthogonality properties
Table 18.3.1
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Poisson kernels
§18.18(vii)
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recurrence relations
Table 18.9.1
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relations to other functions
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Rodrigues formula
Table 18.5.1
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special values
Table 18.6.1
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symmetry
Table 18.6.1
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tables
§18.41(i)
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upper bounds
§18.14(i)
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zeros §18.16(v), §18.2(vi)
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Hermite–Darboux method
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Hermitian matrices
-
Gaussian unitary ensemble
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limiting distribution of eigenvalues
§32.14
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Heun equation, see Heun’s equation.
-
Heun functions
§31.1
-
Heun polynomials
§31.5
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Heun’s equation
§31.2(i)
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Heun’s operator
§31.10(i)
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hexadecimal number system
§3.1(i)
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high-frequency scattering
-
parabolic cylinder functions
§12.17
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higher-order symbols
§34.11
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highway design
-
Hilbert space
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interrelation between bases
-
orthonormal basis
§31.15(iii)
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Hilbert transform
-
Hill’s equation Ch.28, see also Whittaker–Hill equation.
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Hölder’s inequalities for sums and integrals §1.7(i), §1.7(ii)
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holomorphic function, see analytic function.
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homogeneous harmonic polynomials
§14.30(iv)
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homographic transformation, see bilinear transformation.
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Hurwitz criterion for stable polynomials
§1.11(v)
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Hurwitz system
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Hurwitz zeta function
§25.11
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hydrodynamics
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hyperasymptotic expansions
§2.11(v)
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hyperbola
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hyperbolic cosecant function, see hyperbolic functions.
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hyperbolic cosine function, see hyperbolic functions.
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hyperbolic cotangent function, see hyperbolic functions.
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hyperbolic functions
Ch.4
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hyperbolic secant function, see hyperbolic functions.
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hyperbolic sine function, see hyperbolic functions.
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hyperbolic tangent function, see hyperbolic functions.
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hyperbolic trigonometric functions, see hyperbolic functions.
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hyperbolic umbilic bifurcation set
-
hyperbolic umbilic canonical integral
§36.2(i)
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asymptotic approximations
§36.11—§36.12(iii)
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convergent series
§36.8
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differential equations
§36.10(iii)
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formulas for Stokes set
§36.5(iii)
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integral identity
§36.9
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picture of Stokes set Figure 36.5.9, Figure 36.5.9, Figure 36.5.9
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pictures of modulus Figure 36.3.10, Figure 36.3.10, Figure 36.3.10, Figure 36.3.11, Figure 36.3.11, Figure 36.3.11, Figure 36.3.12, Figure 36.3.12, Figure 36.3.12, Figure 36.3.9, Figure 36.3.9, Figure 36.3.9, Erratum (V1.0.14) for Figures 36.3.9, 36.3.10, 36.3.11, 36.3.12
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pictures of phase Figure 36.3.18, Figure 36.3.18, Figure 36.3.19, Figure 36.3.19, Figure 36.3.20, Figure 36.3.20, Figure 36.3.21, Figure 36.3.21
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scaling laws
§36.6
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zeros
§36.7(iv)
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hyperbolic umbilic catastrophe §36.2(i), §36.5(iv), §36.5(iv)—§36.5(iv)
-
hyperelliptic functions
§22.19(iv)
-
hyperelliptic integrals
§19.16(i)
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hypergeometric differential equation
§15.10(i)
-
hypergeometric equation, see hypergeometric differential equation.
-
hypergeometric function §15.2(i), see also Gaussian hypergeometric function.
-
hypergeometric functions of matrix argument, see confluent hypergeometric functions of matrix argument, Gaussian hypergeometric functions of matrix argument, and generalized hypergeometric functions of matrix argument.
-
hypergeometric -function
§19.16(ii)