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| Srivastava H.M., Manocha H.L. — A Treatise on Generating Functions |
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| Предметный указатель |
Abdul-Halim, N. 248—251 272 275
Abel's summability method 9
Abel, N.H. (1802—1829) 285
Abiodun, R.F.A. 386 454
Accumulation point 20
Agarwal, A.K. 416 449 450 490
Agarwal, R.P. 99 170
Agrawal — Chaubey's problem 447
Agrawal, B.D. 78 447
Agrawal, B.M. 347 348
Airey, J.R. 37
Al-Salam, W.A. 106 162 167 170—172 214 215 248—251 256 272 275 281 411
Analytic continuation 21 26 32 43 221 291 407
Analytic curve 314 315
Analytic homomorphism 319 320
Appell functions 14 52—59 63 69—71 105 109 111 114 115 118 122 150 164 236 343 344
Appell functions, generalized 15
Appell polynomials 9
Appell sets 368 398
Appell, P. (1855—1930) 52 53 56 58 61 63 98 99 119 182 368
Askey, R. 71 82
Asymptotic behaviour 9
Bailey's bilinear generating function 116 117 129 167 473
Bailey's formula 109 117
Bailey's identities 385
Bailey, W.N. (1893—1961) 31 54 84 89 92 93 96 112 116 130 194 295
Barnes, E.W. (1874—1953) 49
Basu, D.K. 413
Bateman polynomials 9 14 15 17 183 184
Bateman polynomials, generalized 14 183
Bateman polynomials, generating function for 183
Bateman's formula 167
Bateman's k-function 15 40
Bateman, H. (1882—1946) 167 183—185
Beckmann, P. 71
Bedient polynomials 9 14 16 186
Bedient polynomials, generating function for 186
Bedient, P.E. 186
Beightler, C.S. 195
Bell polynomials 9 397
Bell polynomials general 13
Bell, E.T. (1883—1960) 77
Bellandi Fo, J. 453
Bernoulli numbers 13
Bernoulli numbers, generating function for 85
Bernoulli polynomials 9 13
Bernoulli polynomials, generalized 13 397
Bernoulli polynomials, generating function for 85 397
Bessel coefficients 475
Bessel functions 9 15 39 44 47 75 85 209 235 311 403 427
Bessel functions, Bessel's integral for 88
Bessel functions, generalized 15 17 50 495
Bessel functions, modified 15 39 44 84 209 253
Bessel polynomials 9 17 75 77 92 252 255 281 386 403 409 412 419 434 448
Bessel polynomials, generalized 16 17 77 419
Bessel polynomials, generating function for 84 139 170 419
Bessel's differential equation 332
beta function 17 19 25
Beta function incomplete 17 27 35
Beta transformation 284
Bhagchandani, L.K. (1944—1969) 259 283
Bhargava, S.K. 78 448
Bhati, S.S. 258 259 451 467
Bhattacharya, S.L. 145
Bhise, V.M. 181
Bhonsle, B.R. 93 259
Binomial coefficients 17 22
Binomial expansion 356
Binomial theorem 356 406
Biorthogonal polynomials see "Konhauser polynomials"
Boas, R.P., Jr. 368
Bochner, S. (1899—1982) 49
Boersma, J. 50
Bottema, O. 187
Braaksma, B.L.J. 50
Brafman polynomials 9 13 198 361 444
Brafman polynomials, generating function for 136 137 194 444
Brafman's formula 137 146
Brafman's result 167
Brafman, F. (1923—1959) 76 93 109 110 136—138 141 166 184 185 223 228 275 403 442
Bragg, L.R. 426 444
Branch point 13
Brown's generating functions 361 390
Brown's result 359 363 367
Brown, J.W. 196 357 358 361 365 368 385 395
Buchholz, H. 171 172 250 251 279
Burchnall's generating function 141 167
Burchnall, J.L. (1892—1975) 55 63 84 170 300
Buschman, R.G. 56 97 98 284 368—371 373—375 394—396 459—461 492 493
Calvez, L.C. 194 195 198 359 381 388 401 433
Carlitz — Srivastava result 465
Carlitz's formula 89 234
Carlitz's result 92 358 378 381 382 386
Carlitz's theorem 375 378
Carlitz, L. 11 61 82 84 120 150 184 275 279 354 356 359 376—378 386 396—398 402 432 437 452 462—467 493—497
Carlson, B.C. 56 61 71 194 210—212
Casimir eigenvalue equation 344 345
Casimir operator 328
Cauchy — Hadamard theorem 404
Cauchy's integral formula 88 287 405
Cesaro polynomials 9 14 403 449
Cesaro's summability method 9
Chak, A.M. 77 245 462 464 495
Chakrabarty, A.B. 353
Chandel, R.C.S. 78 259 401 448
Chatterjea, S.K. 77 245 246 279 348 385 388 389 411 413 414 416 425 437 451 452 467 497
Chaubey, J.P. 78 447
Chaundy's formula 139 141 231 373
Chaundy's generating function 141 183 198 228
Chaundy's result 138 140 212 229 247 352
Chaundy, T.W. (1889—1966) 63 138 140 166 205 209 300
Chen, M.P. 348
Chihara, T.S. 71
Chiney, S.P. 348
Choe, Y.H. 264 265
Chongdar, A.K. 348
Chu — Vandermonde theorem 31
Chu, Shih-chieh (flourished 1280—1303) 31
Cigler, J. 378
Classical orthogonal polynomials see "orthogonal polynomials"
Cohen, M.E. 130 180 189 377 384 396 400 453 467
Cohn, P.M. 311
Combinatorial identity 355—358 360 456 492
Combinatorial method 10
Commutation relations 321 340 343
Confluent hypergeometric equation 36
Confluent hypergeometric functions 14 16 17 18 36
Confluent hypergeometric functions of n (or several) variables 62 468
Confluent hypergeometric functions of three variables 223
Confluent hypergeometric functions of two variables 58 132
Contour integration 10 27
Copson, E.T. (1901—1980) 27
Cubic transformations 33
D'Alembert's ratio test 30 404
Danese, A.E. 71
Daoust, M.C. 64 65 147 166 167 192 264 266
Darboux's method 9
Das, M.K. 348 411 451
De Moivre, A. (1667—1754) 23
Derivative operator 10
Deshpande, V.L. 181 182 272
di Oliveira, E.C. 453
Difference equations 9
Differential operator 238 239 242 320 323 324 327 340 368 370 467 502
Dixon's theorem 236
Dixon, A.L. (1867—1955) 49
Doetsch, G. 172
Duplication formula 23
Dwivedi, B.N. 259
E-function 14 19 45
| Elliptic integrals, complete 14 16 35
Entire function 27
Equivalence theorem 403
Erdelyi's expansion 260
Erdelyi's formula 160 236
Erdelyi's generalization 467
Erdelyi's result 149 237
Erdelyi, A. (1908—1977) 31 34 38 39 45 48—50 54 56 58 71 96 105 116 126 133 185 202 205 219—222 236 239 259 260 273 275 279 284 287 293 344 425 441 464 495
Error functions 13 28 40
Error functions complementary 13 28
Essential singularity 20
Euler numbers 14
Euler numbers, generating function for 85
Euler polynomials 9 13
Euler polynomials, generalized 14 397
Euler polynomials, generating function for 85 397
Euler transform 248 284
Euler transform, generalized 18
Euler — Mascheroni constant 17 20
Euler's integral representation 31 34
Euler's transformation 33 95 106 111 117 120 225 243 299 470 472
Euler, L. (1707—1783) 19 285
Eulerian integral 25 218 221
Exton, H. 54 61 65 235 276 489 495
f-function 468
Factorial function 19 21 22
Fasenmyer polynomials 9 182
Fasenmyer, Sister M.C. 182 183
Feldheim's formula 220 257
Feldheim, E. 94 170 171 257 261
Feng, C.C. 348
Ferrar, W.L. 49
Fields, J.L. 278
Flensted-Jensen, M. 453
Foata, D. 82 467
Fourier, J.B.J. (1768—1830) 285
Fox's H-function 15 45
Fox, C. (1897—1977) 49
Fractional derivative 284 285 303 304
Fractional derivative Riemann — Liouville 13 286 287
Fractional derivative Weyl 13 287
Frink, O. 75 409
Fujiwara, I. 388 389
Functional equation 10
G-function 15 19 45—48 50 454
Gamma function 17 19
Gamma function incomplete 27 40
Gauss's multiplication theorem 23 136
Gauss's summation theorem 30 54 61
Gauss, C.F. (1775—1855) 19 20 30
Gaussian hypergeometric function 14 29 228 334
Gegenbauer function 13 188
Gegenbauer polynomials 9 13 71 74 77 89 100 125 137 403 409 412 413 419 450 453
Gegenbauer polynomials, differential equation for 72
Gegenbauer polynomials, generating function for 83 110 125—131 212 419 450
Gegenbauer polynomials, hypergeometric representation for 35
Gegenbauer polynomials, orthogonality property for 72
Gegenbauer polynomials, recurrence relation for 72
Gegenbauer polynomials, Rodrigues formula for 72
Gegenbauer, L. (1849—1903) 9
Generalized Gauss (and Kummer) series 41
Generating function see "sequences"
Generating function bilateral 79
Generating function bilinear 79
Generating function divergent 78
Generating function linear 78
Generating function multilateral 80 81
Generating function multilinear 80 81
Generating function multiple 81
Generating function multivariable 80
Genin, R. 194 195 198 359 381 388 401 433
Geometric series 29
Glaisher's operational formula 446
Glaisher, J.W.L. (1848—1928) 446
Goldberg, J.L. 368
Gottlieb polynomials 9 16 185 403 449
Gottlieb polynomials, generating function for 186 449
Gottlieb, M.J. 185 186
Gould — Hopper generalization 429
Gould — Hopper polynomials 9 15 76 138 361 430 434 446
Gould — Hopper polynomials, generating function for 194
Gould's identity 10 354 356 373 386 400 458 460 479
Gould, H.W. 76 77 86 354 356 385 429
Goursat,E. J.B. (1858—1936) 54
Goyal, G.K. 236
Goyal, S.P. 51 66 180
Grosswald, E. 75 170
Group-theoretic methods 223
Group-theoretic study 353
Guggenheimer, H.W. 311
Gupta's result 241 243
Gupta, K. 239 240 242
Gupta, K.C. 51 66 180 258
Gupta, R.P. 76 77
H-function 15 19 45 49—51 258 259 454 465
Hahn polynomials 16 75
Haimo, D.T. 426 444
Handa, S. 258
Hansen, E.R. 130 273 279 419
Hardy, G.H. (1877—1947) 84
heat polynomials, generalized 16 426 444
Helgason, S. 311
Hermite function 311
Hermite polynomials 9 15 71 74 76 380 381 396 398 403 409 412 419 429 430 434 446 455 467
Hermite polynomials, differential equation for 74
Hermite polynomials, even and odd 75
Hermite polynomials, generalized 15 86
Hermite polynomials, generating function for 83 86 138 194 381 419
Hermite polynomials, hypergeometric representation for 40 41
Hermite polynomials, orthogonality property for 73
Hermite polynomials, recurrence relation for 74
Hermite's method 10
Hermite, C. (1822—1901) 9
Hille — Hardy formula 84 150 187 222 273 333 447 467
Hille, E. (1894—1980) 84
Holomorphic function 403
Homomorphism 319
Hopper, A.T. 76 77 429
Horn's functions 15 57 70 71 311 343
Horn, J. (1867—1946) 54 56 343
Hudson, D.L. 384
Hull, T.E. 311
Humbert functions 17 18 63 132
Humbert polynomials 15 77
Humbert polynomials, generalized 16 86
Humbert polynomials, generating function for 86
Humbert's notation 17 39
Humbert, P. (1891—1953) 37 58 63
Hypergeometric equation 29 36 334 345
Hypergeometric equation confluent 36
Hypergeometric function 14 31 75 311 343
Hypergeometric function confluent 14 16—18 36
Hypergeometric function Gaussian 14 334
Hypergeometric function, generalized 14 18 41 42 50 219 248 465
Hypergeometric functions of n (or several) variables 14 17 18 60
Hypergeometric functions of three variables 14 15 18 68—70
Hypergeometric functions of two variables 14 17 18 52 56 58 63 343
Hypergeometric polynomials 75 360
Hypergeometric polynomials, generalized 14 15 42 76 136 138 182 218 259 358 366 454
Hypergeometric representations see "functions"
Hypergeometric representations of classical orthogonal polynomials 71
Hypergeometric representations of elementary functions 34 44
Hypergeometric representations of other functions 34—36 44 45
Hypergeometric series 14 30 201
Hypergeometric series, generalized 200
Infeld, L. 311
Infinitesimal vectors 314 315
Integral equations 284
Integral function 27
Irregular singularity 36
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