|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Bell W.W. — Special Functions for scientists and engineers |
|
|
|
| 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
|
|
|
| Реклама |
|
|
|
|
|
|
|
|
О проекте