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Bell W.W. — Special Functions for scientists and engineers
Bell W.W. — Special Functions for scientists and engineers

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Название: Special Functions for scientists and engineers

Автор: Bell W.W.

Язык: en

Рубрика: Математика/Справочники/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1968

Количество страниц: 247

Добавлена в каталог: 05.11.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Associated Laguerre polynomials      176
Associated Laguerre polynomials, definition of      176
Associated Laguerre polynomials, generating function for      177
Associated Laguerre polynomials, notation for      182
Associated Laguerre polynomials, orthogonality properties of      178
Associated Laguerre polynomials, recurrence relations for      178
Associated Legendre equation      62
Associated Legendre functions      62
Associated Legendre functions, definition of      62
Associated Legendre functions, orthogonality relations for      66
Associated Legendre functions, properties of      65
Associated Legendre functions, recurrence relations for      68
Bessel functions      92
Bessel functions of the first kind      94
Bessel functions of the first kind, asymptotic behaviour of      127
Bessel functions of the first kind, definition of      94
Bessel functions of the first kind, generating function for      99
Bessel functions of the first kind, graph of      134
Bessel functions of the first kind, integral representations for      101
Bessel functions of the first kind, orthogonality properties of      137
Bessel functions of the first kind, recurrence relations for      104
Bessel functions of the second kind      97
Bessel functions of the second kind, asymptotic behaviour of      127
Bessel functions of the second kind, definition of      97
Bessel functions of the second kind, explicit expression for      98
Bessel functions of the second kind, graph of      134
Bessel functions of the second kind, recurrence relations for      106
Bessel functions of the third kind      see Hankel functions
Bessel series      141
Bessel's equation      92
beta function      23
Beta function, definition of      23
Chebyshev polynomials      187
Chebyshev polynomials, definition of      187
Chebyshev polynomials, generating function for      190
Chebyshev polynomials, orthogonality properties of      192
Chebyshev polynomials, recurrence relations for      193
Chebyshev polynomials, series for      188
Chebyshev polynomials, special values of      192
Chebyshev's equation      189
Confluent hypergeometric equation      210 212
Confluent hypergeometric function      203
Confluent hypergeometric function, contiguity relations for      212
Confluent hypergeometric function, definition of      203
Confluent hypergeometric function, integral representation of      211
Cosine integral      219
Debye functions      224
Differential equations satisfied by various special functions      233
Differential equations, solution of by Frobenius' method      1
Elliptic integrals      224
Error function      221
Euler's constant      231
Exponential integral      218
Fresnel integrals      221
Frobenius' method      1
Frobenius' method, summary of      7
Gamma function      23
Gamma function, definition of      23 30
Gamma function, graph of      31
Gauss's equation      207
Gegenbauer polynomials      197
Gegenbauer polynomials, definition of      197
Gegenbauer polynomials, differential equation satisfied by      198
Gegenbauer polynomials, generating function for      197
Gegenbauer polynomials, orthogonality properties of      198
Gegenbauer polynomials, power series for      198
Gegenbauer polynomials, recurrence relations for      198
Generating function      236
Generating function for associated Laguerre polynomials      177
Generating function for Bessel functions of the first kind      99
Generating function for Chebyshev polynomials      190
Generating function for Gegenbauer polynomials      197
Generating function for Hermite polynomials      157
Generating function for Jacobi polynomials      198
Generating function for Laguerre polynomials      169
Generating function for Legendre polynomials      46
Hankel functions      107
Hankel functions, asymptotic behaviour of      127
Hankel functions, definition of      107
Hankel functions, recurrence relations for      108
Hermite polynomials      156
Hermite polynomials, definition of      157
Hermite polynomials, generating function for      157
Hermite polynomials, orthogonality properties of      161
Hermite polynomials, recurrence relations for      162
Hermite polynomials, special values of      160
Hermite's equation      156
Hypergeometric equation      207 208
Hypergeometric functions      203
Hypergeometric functions, contiguity relations for      210
Hypergeometric functions, definition of      203
Hypergeometric functions, integral representation of      207
Hypergeometric functions, relationship with other special functions      204
Incomplete gamma functions      218
Indicial equation      3
Integral representation of Bessel functions      101
Integral representation of confluent hypergeometric function      211
Integral representation of hypergeometric function      207
Integral representation of Legendre polynomials      49
Integral representation of modified Bessel functions      116
Integrals involving Bessel functions      141
Jacobi polynomials      198
Jacobi polynomials definition of      198
Jacobi polynomials, differential equation satisfied by      199
Jacobi polynomials, generating function for      198
Jacobi polynomials, orthogonality properties of      199
Jacobi polynomials, recurrence relations for      199
Jacobi polynomials, series for      199
Kelvin's functions      120
Kelvin's functions, graphs of      137
Kummer function      204
Kummer's equation      210
l'Hopital's rule      39 97
Laguerre polynomials      168
Laguerre polynomials, definition of      169
Laguerre polynomials, generating function for      169
Laguerre polynomials, notation for      182
Laguerre polynomials, orthogonality properties of      172
Laguerre polynomials, recurrence relations for      173
Laguerre polynomials, special values of      171
Laguerre's equation      168
Laplace's integral representation      49
Legendre duplication formula      29
Legendre functions of the second kind      70
Legendre functions of the second kind, graphs of      84 85
Legendre functions of the second kind, properties of      77
Legendre polynomials      42
Legendre polynomials, definition of      46
Legendre polynomials, generating function for      46
Legendre polynomials, graphs of      82 83 84
Legendre polynomials, Laplace's integral representation for      49
Legendre polynomials, orthogonality properties of      52
Legendre polynomials, recurrence relations for      58
Legendre polynomials, Rodrigues' formula for      48
Legendre polynomials, special values of      50
Legendre series      55
Legendre's associated equation      62
Legendre's equation      42
Leibniz's theorem      63
Logarithmic integral      219
Modified Bessel functions      110
Modified Bessel functions, asymptotic behaviour of      128
Modified Bessel functions, graphs of      135
Modified Bessel functions, integral representations for      116
Modified Bessel functions, recurrence relations for      113
Neumann functions      see Bessel functions of the second kind
Neumann's formula      78
Orthogonality properties      234
Orthogonality properties of associated Laguerre polynomials      178
Orthogonality properties of associated Legendre functions      66
Orthogonality properties of Bessel functions      137
Orthogonality properties of Chebyshev polynomials      192
Orthogonality properties of Gegenbauer polynomials      198
Orthogonality properties of Hermite polynomials      161
Orthogonality properties of Jacobi polynomials      199
Orthogonality properties of Laguerre polynomials      172
Orthogonality properties of Legendre polynomials      52
Orthogonality properties of spherical harmonics      80
Pochhammer symbol      203
Rayleigh's formulae      126
Recurrence relations for associated Laguerre polynomials      178
Recurrence relations for associated Legendre functions      68
Recurrence relations for Bessel functions of the first kind      104
Recurrence relations for Bessel functions of the second kind      106
Recurrence relations for Chebyshev polynomials      193
Recurrence relations for Gegenbauer polynomials      198
Recurrence relations for Hankel functions      108
Recurrence relations for Hermite polynomials      162
Recurrence relations for Jacobi polynomials      199
Recurrence relations for Laguerre polynomials      173
Recurrence relations for Legendre polynomials      58
Recurrence relations for modified Bessel functions      113
Recurrence relations for spherical Bessel functions      122
Riemann's zeta function      223
Rodrigues' formula      48
Sine integral      219
Spherical Bessel functions      121
Spherical Bessel functions, asymptotic behaviour of      128
Spherical Bessel functions, graphs of      136
Spherical Bessel functions, Rayleigh's formulae for      126
Spherical Bessel functions, recurrence relations for      122
Spherical harmonics      78
Spherical harmonics, orthogonality properties of      80
Ultraspherical polynomials      see Gegenbauer polynomials
Weber — Hermite functions      163
Whittaker's confluent hypergeometric functions      212
Zeta function      223
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