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Luke Y.L. — Special Functions and Their Approximations. Volume II

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Название: Special Functions and Their Approximations. Volume II

Автор: Luke Y.L.

Аннотация:

These volumes are designed to provide scientific workers with a self-contained and unified development for many of the mathematical functions which arise in applied problems, as well as the attendant mathematical theory for their approximations. These functions are often called the special functions of mathematical physics or more simply the special functions.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1969

Количество страниц: 506

Добавлена в каталог: 17.11.2013

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Предметный указатель

Expansion, G-function, JP      II 15 17—19 22—28
Expansion, G-function, LP      II 16—19
Expansion, G-function, other G-functions      I 147 148 152—157 183—189 II 14—24
Expansion, gamma function and derivatives      see also "Expansion incomplete
Expansion, gamma function and derivatives, $ln \Gamma(x+b)$ , $\phi^{(m)}(x+b)$ , CP      I 28 29 II 287
Expansion, gamma function and derivatives, $[\Gamma(x+1)]^{-1}$ , $\Gamma(x+1)$ , CP      I 28 29 II 287 300
Expansion, gamma function and derivatives, $[\Gamma(z+3)]^{-1}$ , $\Gamma(z+3)$ , powers of z      I 26—28 II 299
Expansion, gamma function and derivatives, $\Gamma(x+3)$ , $ln \Gamma(x+3)$ , $\psi^{(m)}(x+3)$ , CP      I 28 29 II 287 301—303
Expansion, gamma function and derivatives, $\Gamma(z+1)$ , series of $[(z+1)_{n}(z+1)_{-n}]^{-1}$       II 304 305
Expansion, hypergeometric function, confluent, the $\psi$ -function, CP      II 25 28 238—240
Expansion, hypergeometric function, confluent, the $\psi$ -function, G-functions      II 25
Expansion, hypergeometric function, confluent, the $_{1}F_{1}$ , BF      I 129—133 II 48 209
Expansion, hypergeometric function, confluent, the $_{1}F_{1}$ , CP      II 35
Expansion, hypergeometric function, confluent, the $_{1}F_{1}$ , JP      II 48
Expansion, hypergeometric function, Gaussian, the $_{2}F_{1}$ , $_{1}F_{1}$ 's      I 130
Expansion, hypergeometric function, Gaussian, the $_{2}F_{1}$ , CP      II 34
Expansion, hypergeometric function, Gaussian, the $_{2}F_{1}$ , JP      II 62
Expansion, hypergeometric function, Gaussian, the $_{2}F_{1}$ , other $_{2}F_{1}$ 's      II 62—64
Expansion, hypergeometric function, generalized, the $_{p}F_{q}$ , BF      II 44 45 58—61
Expansion, hypergeometric function, generalized, the $_{p}F_{q}$ , CP      I 296 II 30 31
Expansion, hypergeometric function, generalized, the $_{p}F_{q}$ , GP      II 29 30
Expansion, hypergeometric function, generalized, the $_{p}F_{q}$ , JP      II 1—8 13 29 44 45
Expansion, hypergeometric function, generalized, the $_{p}F_{q}$ , LP      II 9—12 14 44
Expansion, hypergeometric function, generalized, the $_{p}F_{q}$ , other $_{p}F_{q}$ 's      II 1—14 29—31 64 65
Expansion, incomplete gamma function, $\gamma(\nu, z)$ , BF      II 55 56 289
Expansion, incomplete gamma function, $\gamma(\nu, z)$ , CP      II 40 41 55 56 see sine "Expansion error "Expansion exponential "Expansion Fresnel "Expansion hypergeometric "Expansion confluent"
Expansion, inverse tangent integral, t-1 arc tan t dt, CP      II 310
Expansion, ker, kei, and derivatives      I 216 see
Expansion, Laplace transform, inverse of, by expansion of desired function in series of Jacobi, Laguerre, and other orthogonal polynomials      II 247—251
Expansion, Legendre polynomial, BF      I 279
Expansion, logarithm, $ln\{x+(x^{2}+1)^{1/2}\}$ , CP      II 312
Expansion, logarithm, dilogarithm, $\int_{0}^{x} t^{-1} ln(1+t) dt$ , CP      II 310
Expansion, logarithm, ln(1+0.16x), CP      II 288
Expansion, logarithm, ln(1+x), CP      II 308
Expansion, logarithm, ln(a+z), $_{2}F_{1}$ ’s      II 63
Expansion, logarithm, ln(a+z), CP      II 31 288 308
Expansion, logarithm, ln(a+z), JP      II 13
Expansion, logarithm, ln{(1+z)/(1-z)}, series of $[1-(1-z^{2})^{1/2}]^{n}/z^{n}$       II 63
Expansion, Lommel functions, BF      II 39 54 55
Expansion, Lommel functions, CP      II 27 39
Expansion, Lommel functions, GP      II 39
Expansion, powers of z, $(1+x)^{-1}$ , $(1+x^{2})^{-1/2}$ , CP      II 307
Expansion, powers of z, $(1-k^{2} sin^{2}\theta)^{\omega}$ , $cos 2n\theta$ , and $_{2}F_{1}$ 's      II 35
Expansion, powers of z, $x^{m}T^{*}_{n}(x)$ , CP      I 301
Expansion, powers of z, $x^{m}T_{n}(x)$ , CP      I 298
Expansion, powers of z, $x^{\mu}e^{xz}$ , BF      II 45 46
Expansion, powers of z, $x^{\mu}e^{xz}$ , JP      I 285
Expansion, powers of z, $z^{m}$ , m a positive integer or zero, $_{p}F_{q}$ 's      II 6 7 11—13
Expansion, powers of z, $z^{m}$ , m a positive integer or zero, CP      II 295 298
Expansion, powers of z, $z^{m}$ , m a positive integer or zero, JP      I 277 291 II 6 7 14
Expansion, powers of z, $z^{m}$ , m a positive integer or zero, LP      II 11
Expansion, powers of z, $z^{\mu}$ , $_{p}F_{q}$ 's      II 2 5 9 14 31
Expansion, powers of z, $z^{\mu}$ , BF      II 45 46
Expansion, powers of z, $z^{\mu}$ , JP      I 284 285 II 2 5 20 31
Expansion, powers of z, $z^{\mu}$ , LP      II 9
Expansion, Psi( $\psi$ )-function or logarithmic derivative of the gamma function      see "Expansion gamma
Expansion, sine and cosine integrals, $\int_{0}^{x} t^{-1} sin t dt$ , $\int_{0}^{x} t^{-1} (1 - cos t) dt$ , CP      II 42 289 325
Expansion, sine and cosine integrals, $\int_{0}^{z} t^{-\alpha} sin t dt$ , $\int_{0}^{z} t^{-\alpha} (\alpha - cos t) dt$ , a=0, 1      BF II 42 56 57 289
Expansion, sine and cosine integrals, $\int_{x}^{\infty} t^{-1} sin t dt$ , $\int_{x}^{\infty} t^{-1} cos t dt$ , CP      II 27 289 326 327
Expansion, sine and cosine, $z^{-1}(1-cos z)$ , BF      II 47
Expansion, sine and cosine, $z^{-1}(1-cos z)$ , CP      II 34
Expansion, sine and cosine, $z^{\lambda} sin z$ , $z^{\lambda} cos z$ , BF      II 32 33 46 47
Expansion, sine and cosine, hyperbolic, CP      II 313 314 363
Expansion, sine and cosine, hyperbolic, inverse of, CP      II 312
Expansion, sine and cosine, inverse of, CP      II 288 311
Expansion, sine and cosine, sin z, cos z, CP      II 33 34 288 316—319 354
Expansion, sine and cosine, sin z, cos z, Legendre polynomials      II 288
Expansion, Struve functions, $H_{n}(x),$ H_{n}(x)-Y_{n}(x}$, n=0, 1      CP 370 371
Expansion, Struve functions, $H_{\nu}(z)$ , $L_{\nu}(z)$ , BF      II 40 55
Expansion, Struve functions, $L_{n}(x)$ , n=0, 1, CP      II 374
Expansion, Struve functions, integrals of, $\int_{0}^{x} t^{-m} H_{0}(t) dt$ dt, m=0, 1, BF      II 40
Expansion, Struve functions, integrals of, $\int_{0}^{x} t^{-m} H_{0}(t) dt$ dt, m=0, 1, CP      II 40 372
Expansion, Struve functions, integrals of, $\int_{0}^{x} t^{-m} L_{0}(t) dt$ , m=0, 1      CP II 375
Expansion, Struve functions, integrals of, $\int_{0}^{x} t^{-m} [H_{0}(t)-Y_{0}(t)] dt$ , m=0, 1, CP      II 373
Expansion, tangent and cotangent, hyperbolic, inverse of, CP      II 312
Expansion, tangent and cotangent, inverse of, arc tan x, CP      II 32 288 309
Expansion, tangent and cotangent, inverse of, arc tan x, series of $[(1+x^{2})^{1/2}-1]^{n}/x^{n}$       II 63
Expansion, tangent and cotangent, inverse tangent integral, $\int_{0}^{x} t^{-1} arc tan t dt$ , CP      II 310
Expansion, tangent and cotangent, tan x, cot x, CP      II 33 320
Expansion, tangent and cotangent, tan x, cot x, series of $[4m^{2}-z^{2}]^{-1}$       II 33
Expansion, Weber function      see "Anger — Weber"
Expansion, Whittaker functions      see "Expansion hypergeometric confluent"
Expansion, Zeta function, $x\zeta(1+x)$ and related functions, CP      II 287 306
Exponential function      I 38 40 48 209 II 195 257 292 see "Expansion"
Exponential integral      I 3 7 135 221 222 II 201 see "Expansion"
Fermi — Dirac integrals      II 291
Fresnel integrals      I 135 224 227 see "Expansion"
G-function      I 136—208
G-function, analytic continuation      I 148 149 194
G-Function, approximation of, by polynomials and rational functions      see "Approximation"
G-Function, asymptotic expansion, exponential, recurrence formula for coefficients in      I 200 202 205—208
G-function, asymptotic expansion, large parameter      II 23 24 26 27
G-Function, asymptotic expansion, large variable      I 178—180 189—194
G-function, definition      I 139 142—145
G-function, differential equation and solutions      I 181 182
G-function, elementary properties      I 149—152
G-Function, expansions of, in series of, G-functions      I 147 148 152—157 183—189 II 24 see
G-Function, expansions of, in series of, generalized hypergeometric functions      I 139 142 145—147 see
G-function, expressed as a named function      I 230—234
G-function, hypergeometric functions and named functions, connection with      I 225—234
G-function, integral representations      I 59 143—145 159 164—175 177 II 23
G-Function, integrals involving Euler and related transforms      I 170—177 II 23
G-Function, integrals involving Fourier transform      I 166 169
G-Function, integrals involving Laplace and inverse Laplace transforms      I 166—169
G-Function, integrals involving Mellin and inverse Mellin transforms      I 157—159
G-Function, integrals involving other transform pairs      I 177
G-Function, integrals involving product of two G-functions      I 159—166
G-function, multiplication theorems      I 152—157
G-function, named functions expressed in terms of      I 225—230
Gamma function      I 8—37 see
Gamma function, analytic continuation      I 10 11
Gamma function, approximation      see "Approximation"
Gamma function, asymptotic expansion, $\Gamma (z)$ and $ln \Gamma (z)$       I 31—33
Gamma function, asymptotic expansion, ratio of products of gamma functions      I 33—37
Gamma function, asymptotic expansion, recurrence formula for coefficients in asymptotic expansion for ratio of products of gamma functions      I 205—208
Gamma function, definite integrals expressed in terms of      I 15 16 60 61 157 177
Gamma function, definition and elementary properties      I 8—10
Gamma function, expansion      see "Expansion"
Gamma function, integral representations      I 8 14—18
Gamma function, logarithmic derivative of      see "Psi-function"
Gamma function, multiplication formula      I 11 12
Gamma function, numerical values for certain fractional arguments      II 293
Gamma function, power series and other expansions      I 26—31
Gegenbauer polynomial      I 273 279
GP      see "Gegenbauer or ultraspherical polynomials"
h-transform      I 165
Hankel functions      I 135 204 213 215 230 234 II 27
Hankel transform      I 165 287
Hermite polynomials      I 135 273 II 245
Hypergeometric function (confluent), $_{1}F_{1}$       see «G-function" "Hypergeometric "Hypergeometric "Incomplete
Hypergeometric function (confluent), $_{1}F_{1}$ , $\psi$ -function, Whittaker functions      I 115—134
Hypergeometric function (confluent), $_{1}F_{1}$ , approximation of, by polynomials and rational functions      see "Approximation"
Hypergeometric function (confluent), $_{1}F_{1}$ , asymptotic expansion, large parameter(s)      I 129 133 134 II 200
Hypergeometric function (confluent), $_{1}F_{1}$ , asymptotic expansion, large variable      I 127 128
Hypergeometric function (confluent), $_{1}F_{1}$ , asymptotic expansion, uniform, large parameters and variable      II 203 204 207 208 210 211
Hypergeometric function (confluent), $_{1}F_{1}$ , confluence principle      I 48
Hypergeometric function (confluent), $_{1}F_{1}$ , contiguous relations      I 48 118 119 126
Hypergeometric function (confluent), $_{1}F_{1}$ , definition      I 40 47 49
Hypergeometric function (confluent), $_{1}F_{1}$ , difference-differential properties      I 48 117—119 125 126
Hypergeometric function (confluent), $_{1}F_{1}$ , differential equation      I 119 120
Hypergeometric function (confluent), $_{1}F_{1}$ , differential equation, solutions, complete      I 121—124
Hypergeometric function (confluent), $_{1}F_{1}$ , differential equation, solutions, degenerate      I 120 121
Hypergeometric function (confluent), $_{1}F_{1}$ , differential equation, solutions, logarithmic      I 122 123
Hypergeometric function (confluent), $_{1}F_{1}$ , differential equation, solutions, ordinary      I 119
Hypergeometric function (confluent), $_{1}F_{1}$ , elementary relations      I 117—119
Hypergeometric function (confluent), $_{1}F_{1}$ , evaluation of a certain $_{1}F_{1}$ for special value of argument      I 113
Hypergeometric function (confluent), $_{1}F_{1}$ , expansions in series of Jacobi polynomials, Chebyshev polynomials, etc.      see "Expansion"
Hypergeometric function (confluent), $_{1}F_{1}$ , expressed as named function      I 224
Hypergeometric function (confluent), $_{1}F_{1}$ , G-function, connection with      I 225 226 228 231 234
Hypergeometric function (confluent), $_{1}F_{1}$ , integral representations      I 115—117

Hypergeometric function (confluent), $_{1}F_{1}$ , Kummer relations      I 121 124—126
Hypergeometric function (confluent), $_{1}F_{1}$ , Laguerre and Hermite polynomial, connection with      I 273
Hypergeometric function (confluent), $_{1}F_{1}$ , named functions expressed in terms of      I 211—213 220—224
Hypergeometric function (confluent), $_{1}F_{1}$ , other notations and related functions      I 134 135
Hypergeometric function (confluent), $_{1}F_{1}$ , products      I 211 228 233 234
Hypergeometric function (confluent), $_{1}F_{1}$ , Wronskians      I 124
Hypergeometric function (confluent), $_{1}F_{1}$ , zeros of $_{1}F_{1}(a,c,z)$       II 208—210
Hypergeometric function (Gaussian), $_{2}F_{1}$       I 38—114 see
Hypergeometric function (Gaussian), $_{2}F_{1}$ , analytic continuation      I 68—71
Hypergeometric function (Gaussian), $_{2}F_{1}$ , approximation of, by polynomials and rational functions      see "Approximation"
Hypergeometric function (Gaussian), $_{2}F_{1}$ , asymptotic expansions for large parameter(s)      I 235—242
Hypergeometric function (Gaussian), $_{2}F_{1}$ , confluence principle      I 49
Hypergeometric function (Gaussian), $_{2}F_{1}$ , contiguous relations      I 47 89
Hypergeometric function (Gaussian), $_{2}F_{1}$ , convergence of series      I 65 68
Hypergeometric function (Gaussian), $_{2}F_{1}$ , definition      I 39 41
Hypergeometric function (Gaussian), $_{2}F_{1}$ , difference-differential properties      I 44—47 88 275 276
Hypergeometric function (Gaussian), $_{2}F_{1}$ , differential equation      I 64 93
Hypergeometric function (Gaussian), $_{2}F_{1}$ , differential equation, solutions, complete      I 65 72—84
Hypergeometric function (Gaussian), $_{2}F_{1}$ , differential equation, solutions, degenerate      I 65 66 69 77—84
Hypergeometric function (Gaussian), $_{2}F_{1}$ , differential equation, solutions, logarithmic      I 75—84
Hypergeometric function (Gaussian), $_{2}F_{1}$ , differential equation, solutions, ordinary      I 64 65 67—71
Hypergeometric function (Gaussian), $_{2}F_{1}$ , elementary relations      I 44—46
Hypergeometric function (Gaussian), $_{2}F_{1}$ , evaluation of, for special values of argument      I 99—103 114
Hypergeometric function (Gaussian), $_{2}F_{1}$ , expansions in series of Jacobi polynomials, other $_{2}F_{1}$ 's, etc.      see "Expansion"
Hypergeometric function (Gaussian), $_{2}F_{1}$ , expressed as named function      I 224
Hypergeometric function (Gaussian), $_{2}F_{1}$ , G-function, connection with      I 139
Hypergeometric function (Gaussian), $_{2}F_{1}$ , integral representations      I 57 58 62 63 89—91
Hypergeometric function (Gaussian), $_{2}F_{1}$ , integrals involving      I 170 172—174
Hypergeometric function (Gaussian), $_{2}F_{1}$ , Kummer relations      I 67 68 85—92
Hypergeometric function (Gaussian), $_{2}F_{1}$ , named functions expressed in terms of      I 209—211
Hypergeometric function (Gaussian), $_{2}F_{1}$ , orthogonal polynomials, classical, connection with      I 273
Hypergeometric function (Gaussian), $_{2}F_{1}$ , polynomial      I 40 65 66 91
Hypergeometric function (Gaussian), $_{2}F_{1}$ , quadratic transformations      I 92—98
Hypergeometric function (Gaussian), $_{2}F_{1}$ , truncated series      I 42 109 110
Hypergeometric function (Gaussian), $_{2}F_{1}$ , Wronskians      I 84 85
Hypergeometric function (generalized), $_{p}F_{q}$       I 38—114 115—134 135—208 see "Special
Hypergeometric function (generalized), $_{p}F_{q}$ , analytic continuation      I 149
Hypergeometric function (generalized), $_{p}F_{q}$ , approximation of, by polynomials and rational functions      see "Approximation"
Hypergeometric function (generalized), $_{p}F_{q}$ , asymptotic expansion, exponential, recurrence formula for coefficients in      I 200 202 205—208
Hypergeometric function (generalized), $_{p}F_{q}$ , asymptotic expansion, large parameter(s)      I 51 55 56 133 242—266
Hypergeometric function (generalized), $_{p}F_{q}$ , asymptotic expansion, large variable      I 195—203
Hypergeometric function (generalized), $_{p}F_{q}$ , confluence principle and theorems      I 49 51 53—56
Hypergeometric function (generalized), $_{p}F_{q}$ , contiguous relations      I 48
Hypergeometric function (generalized), $_{p}F_{q}$ , convergence of series      I 43 44
Hypergeometric function (generalized), $_{p}F_{q}$ , definition      I 41 42 136
Hypergeometric function (generalized), $_{p}F_{q}$ , difference-differential properties      I 44 48
Hypergeometric function (generalized), $_{p}F_{q}$ , differential equation      I 136—138 247
Hypergeometric function (generalized), $_{p}F_{q}$ , differential equation, solutions, complete      I 147 148 181 182
Hypergeometric function (generalized), $_{p}F_{q}$ , differential equation, solutions, logarithmic      I 140—143
Hypergeometric function (generalized), $_{p}F_{q}$ , differential equation, solutions, ordinary      I 137—139
Hypergeometric function (generalized), $_{p}F_{q}$ , elementary relations      I 44
Hypergeometric function (generalized), $_{p}F_{q}$ , evaluation of $_{p+1}F_{p}$ for special values of argument      I 26 113 114 257—259 II 136 139 142—144 151 153 154
Hypergeometric function (generalized), $_{p}F_{q}$ , evaluation of $_{p+1}F_{p}$ for special values of argument, p=1      I 99—103 114
Hypergeometric function (generalized), $_{p}F_{q}$ , evaluation of $_{p+1}F_{p}$ for special values of argument, p=2      I 103—111 113 259 II 142
Hypergeometric function (generalized), $_{p}F_{q}$ , evaluation of $_{p+1}F_{p}$ for special values of argument, p=3      I 112—114 II 140
Hypergeometric function (generalized), $_{p}F_{q}$ , evaluation of a certain $_{2}F_{2}$ for special values of argument      I 113
Hypergeometric function (generalized), $_{p}F_{q}$ , expansion theorem for large parameter      I 51 55 56
Hypergeometric function (generalized), $_{p}F_{q}$ , expansions in series of other $_{p}F_{q}$ 's, Jacobi polynomials, etc.      see "Expansion"
Hypergeometric function (generalized), $_{p}F_{q}$ , expressed as named function      I 224 225
Hypergeometric function (generalized), $_{p}F_{q}$ , G-function, connection with      I 139 142 145—147 225 230 231
Hypergeometric function (generalized), $_{p}F_{q}$ , integral representations      I 58—63
Hypergeometric function (generalized), $_{p}F_{q}$ , integrals involving      I 58—62 164 168 169
Hypergeometric function (generalized), $_{p}F_{q}$ , multiplication theorem      I 155
Hypergeometric function (generalized), $_{p}F_{q}$ , named functions expressed in terms of      I 209—224
Hypergeometric function (generalized), $_{p}F_{q}$ , nearly poised      I 103
Hypergeometric function (generalized), $_{p}F_{q}$ , polynomial      I 42 210
Hypergeometric function (generalized), $_{p}F_{q}$ , truncated series      I 42 210
Hypergeometric function (generalized), $_{p}F_{q}$ , well poised      I 103 104
Incomplete gamma function and related functions      I 135 220—224 II 186—213 see "Expansion"
Inequalities for $(1+1/z)^{-1/2}$       II 185
Inequalities for $(1+1/z)^{-\sigma}$       II 180
Inequalities for $x^{1/x}$       II 181
Inequalities for $x^{x}$       II 180
Inequalities for Bessel function ratio, $2(\nu+1)I_{\nu+1}(z)/I_{\nu}(z)$       II 82
Inequalities for beta function (incomplete)      II 178
Inequalities for error functions, $e^{-z}$       II 195
Inequalities for error functions, $\int_{0}^{z}e^{t^{2}} dt$       II 195
Inequalities for error functions, $\int_{z}^{\infty}e^{-t^{2}} dt$       II 201
Inequalities for exponential integral, $\int_{z}^{\infty} t^{-1}e^{-t} dt$       II 201
Inequalities for hypergeometric function, Gaussian, $_{2}F_{1}(1, \sigma ; \rho + 1; x)      II 173 178
Inequalities for incomplete gamma function, $\gamma(\nu, z)$       II 194 195
Inequalities for Jacobi polynomials      I 280
Integral equations, solution of by expansion in series of Chebyshev polynomials of the first kind      see "Expansion"
Integrals      see "Bessel functions integrals see "Expansion"
Integration, numerical      see "Approximation integrals"
Interpolation, inverse      II 231
Inverse tangent integral      II 310
Jacobi function      I 274
Jacobi polynomials, application of in approximation of functions by polynomials and rational functions      II 68 95 98 see
Jacobi polynomials, asymptotic expansion for large order      I 53 54 237 250—259 278 279
Jacobi polynomials, Bessel function, connection with      I 52
Jacobi polynomials, definition and basic properties      I 273—275 280
Jacobi polynomials, difference-differential properties      I 275 276 II 170—172 177 179
Jacobi polynomials, evaluation and estimation of coefficients of given f(x) when expanded in series of      I 286—296
Jacobi polynomials, evaluation and estimation of coefficients of given f(x) when expanded in series of, asymptotic estimates of coefficients      I 293—296
Jacobi polynomials, evaluation and estimation of coefficients of given f(x) when expanded in series of, coefficients as integral transform      I 286—290
Jacobi polynomials, evaluation and estimation of coefficients of given f(x) when expanded in series of, coefficients when f(x) is defined by Taylor series      I 290—293
Jacobi polynomials, expansion of functions in series of      I 283—285 290—293 see
Jacobi polynomials, extended and generalized, asymptotic expansion for large order      I 53 54 247—263 281—283
Jacobi polynomials, extended and generalized, definition      I 247
Jacobi polynomials, extended and generalized, expansion of functions in series of      I 291 292 see
Jacobi polynomials, extended and generalized, generating function      I 254
Jacobi polynomials, extended and generalized, recurrence or difference formula      II 134—142 145—147
Jacobi polynomials, generating functions      I 254 278
Jacobi polynomials, inequalities      I 280
Jacobi polynomials, integrals involving      I 276 277 281—283 286
Jacobi polynomials, numerical integration and inversion of Laplace transforms      II 244 245 247—249 251—253
Jacobi polynomials, orthogonal polynomials, connection with other      I 273
Jacobi polynomials, orthogonality property      I 276
JP      see "Jacobi polynomials including extended and generalized Jacobi polynomials"
K-transform      I 165
Ker and Kei functions      I 216 see "Approximation" "Expansion"
Kontorovich — Lebedev transforms      I 177
Kummer's formula      I 57
Kummer's solution      I 67
Laguerre polynomial, approximation of functions by use of      see "Approximation"
Laguerre polynomial, asymptotic expansion for large order      I 264—266 II 203 207
Laguerre polynomial, confluent hypergeometric function, connection with      I 135
Laguerre polynomial, definition and orthogonality property      I 273
Laguerre polynomial, difference-differential properties      II 198—201
Laguerre polynomial, expansion of functions in series of      I 291 292 see
Laguerre polynomial, generalized and extended, asymptotic expansion for large order      I 263—266
Laguerre polynomial, generalized and extended, definition      I 263
Laguerre polynomial, generalized and extended, expansion of functions in series of      I 291 292 see
Laguerre polynomial, generalized and extended, recurrence or difference formula      II 143 144 147 148
Laguerre polynomial, Jacobi polynomial, connection with      I 273
Laguerre polynomial, numerical integration and inversion of Laplace transforms      II 245 249—251
Laguerre polynomial, zeros of      II 208—210
Laplace transform or integral, Abelian-type theorems      II 246 247
Laplace transform or integral, approximation      see "Approximation"
Laplace transform, inverse of, approximation and expansion      see "Approximation" "Expansion"
Laplace transform, inverse of, Tauberian-type theorems      II 247
Legendre functions      I 178 211 II 165
Legendre polynomials      I 273 279
Logarithm      I 38 40 210 II 292 see "Expansion"
Lommel functions      I 217 218 227 234 see "Expansion"
lp      see "Laguerre polynomials including extended and generalized Laguerre polynomials"
Mathematical constants      II 292 293
Mehler transforms      I 178
Mellin — Barnes integrals, evaluation of by trapezoidal integration rule      II 225
Named functions expressed as $_{p}F_{q}$ 's      I 209—224
Named functions expressed as G-functions      I 225—230
Order symbols      I 1
Orthogonal functions      I 267—270
Orthogonal polynomials      I 267—329 see "Chebyshev "Bessel
Orthogonal polynomials, application to approximation and expansion of functions      see "Approximation" "Expansion"
Orthogonal polynomials, classical, orthogonal properties of      I 273
Orthogonal polynomials, definition and basic properties      I 267—272 II 145
P      see "Polynomial"
Pade approximation      see also "Approximation" "Continued

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