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| Srivastava H.M., Manocha H.L. — A Treatise on Generating Functions |
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| Предметный указатель |
Ismail, M.E.H. 278
Isomorphism 319 320
Jacobi function 16 453
Jacobi polynomials 9 16 71 89 100 125 126 131 152 155 156 200 243 353 388 389 403 409 412 420 432 442 449 453 455 471 473 497
Jacobi polynomials, differential equation for 72
Jacobi polynomials, generating function for 82 83 104—124 146 157 191 201—206 250 252 353 359 420 497
Jacobi polynomials, hypergeometric representation for 35 91 243
Jacobi polynomials, orthogonality property for 71
Jacobi polynomials, recurrence relation for 71
Jacobi polynomials, Rodrigues formula for 71
Jacobi's generating function 110 170 389
Jacobi, C.G.J. (1804—1851) 9
Jain, G.C. 76 77
Jain, P.C. 268
Jain, R 347 348
Jain, R.N. 147 176 179 251—253 272 281 283
Jain, S. 212 280 348 see H.L.; T.R."
Joshi, C.M. 78 256—258 282 283 400 448
k-function 15 40
Kahaner, D. 378
Kalnins, E.G. 311 343
Kampe de Feriet's function 14 64
Kampe de Feriet, J. (1893—1982) 54 56 61 63 98 99 119 164 182
Karande, B.K. 359 389 453
Karlsson, P.W. 65 490 491
Kelvin functions 13 210
Khan, I.A. 141 146 168 176 177
Khandekar, P.R. 139
Kibble, W.F. 467
Konhauser biorthogonal polynomials see "Konhauser polynomials"
Konhauser polynomials 9 17 198 381 432 446 469 499 501
Konhauser, J.D.E. 77 197 381 432
Koornwinder, T. 453
Krall, H.L. 75 409
Krawtchouk polynomials 16 75
Kummer's differential equation 36
Kummer's equation 18
Kummer's first theorem 37 244 257 471
Kummer's function 14 36 37
Kummer's second theorem 37
Kummer, E.E. (1810—1893) 36
Kyriakopoulis, E. 348
l'Hopital, G.A. (1661—1704) 285
Lacroix, S.F. 285
Lagrange expansion 10 354 355 361 377 380 384 389 400 402 407 490
Lagrange polynomials 9 15 403 441 442 452
Lagrange polynomials, generating function for 85 441
Lagrange's extension 82
Lagrange, J.L. (1736—1813) 285
Laguerre function 16 326 339
Laguerre function hypergeometric, representation for 41
Laguerre function, differential equation for 326
Laguerre polynomials 9 16 71 74 77 100 125 200 201 220 242 380 381 403 409 420 430 434 455 467
Laguerre polynomials, differential equation for 74
Laguerre polynomials, generating function for 84 131—136 157 207—209 240 252 381 420
Laguerre polynomials, hypergeometric representation for 41 207 246
Laguerre polynomials, modified 14 425 444
Laguerre polynomials, orthogonality property for 74
Laguerre polynomials, recurrence relation for 74
Laguerre polynomials, Rodrigues formula for 74
Laguerre, E.N. (1834—1886) 9
Laplace transform 16 218 228 229 231 236 237 261 280 358 468
Laplace transform inverse 16 218 229 231 236 261
Laplace transform, generalized 16
Laplace, P.S. (1749—1827) 285
Lardner's formula 210
Lardner, T.J. 210 211
Laurent expansion 88 326 337 479
Laurent series 11 337 345 475 477
Laurent series, generating function involving 81 455 475
Laurent series, multidimensional 484 485
Lauricella functions 14 18 60 62 63 66 68—70 115 117 122 124 125 462 466 473
Lauricella functions, generalized 14 65 190 384 456 481
Lauricella polynomials 9 196 382 401 403 440 464
Lauricella polynomials, generalized 458
Lauricella's conjecture 68
Lauricella's notations 66
Lauricella's set 66
Lauricella, G. (1867—1913) 60 61 66
Lavoie, J.L. 78 90 130 165 285 287 306 307 381 414—417 429 437 441 445—447 452
Lebedev, N.N. 71
Lee, P.A. 425
Legendre function, associated 16 34 35
Legendre function, associated, of the second kind 187 189
Legendre polynomials 9 16 71—73 239 403 409 423 453
Legendre polynomials, generating function for 83 110 377 423
Legendre polynomials, hypergeometric representation for 35
Legendre's duplication formula 23
Legendre, A.M. (1752—1833) 9
Leibniz, G.W. (1646—1716) 285
Leroux, P. 82
Lie algebras 314—317 319—321 324 328 340 343 348 351
Lie groups 311—313 319
Lie product 314 316—318
Lie theoretic method 311
Lie's third fundamental theorem 319
Linear differential equation 29
Linear operators 320 321
Linear transformations 33
Liouville, J. (1809—1882) 285
Lommel functions 16 44 48
Luke, Y.L. (1918—1983) 31 34 45 47 48 71 262
MacRobert's E-function 14 45 47 201
MacRobert, T.M. (1884—1962) 38 201
Madhekar, H.C. 197 198 389 448 473 474 502
Magnus, W. 31 34 38 39 45 48—50 54 56 58 71 96 105 126 133 185 202 205 219—221 236 239 259 273 275 287 293 344 425 441
Maheshwari, N.K. 179
Manocha, B.L. 11 280
Manocha, H.L. 11 99 106 110 112—114 117—120 123 124 130 156 158—160 164 165 169 170 177 181 200 212 214 215 236 279 280 295 307 308 310 311 343 348 416 449 450 490 494
Mathai, A.M. 47 51
Mathur, R. 448
Matrix multiplication 312 313
McBride, E.B. 71 79 311 331 348 419 425
Mehler's formula 83 446 467
Meijer transform, generalized 18
Meijer transformation 253
Meijer's G-function 15 45
Meijer, C.S. (1904—1974) 15
Meixner polynomials 9 75 403 443 449
Meixner's bilinear relations 273—275 309 352
Meixner's formula 244 274 275 295 296 299
Meixner, J. 38 150 223 228 244 275 295—298
Mellin — Barnes contour integral 32 43 45 49
Mellin.H. (1854—1933) 49
Meromorphic function 27
Milch, P.R. 82
Miller, w., jr. 11 311 328 343 348 352
Mittag-Leffler function 13
Mittag-Leffler function, generalized 14
Mittag-Leffler polynomials 9 50 185
Mittag-Leffler polynomials, generating function for 185
Mittag-Leffler, G. (1846—1927) 9
Mittal, H.B. 78 368 370 373 387
Mittal, K.C. 156 441 452
Mitten, L.G. 195
Moser, L. (1921—1970) 184
Multinomial theorem 87
Multiplication theorem 23 136
Multiplier representation 320 321 328 335 340 343 345 346 352
Munot, P.C. 448
Nekrassov, P.A. 287
Nemhauser, G.L. 195
Niukkanen, A.W. 65
Non-commutative operators 453
Oberhettinger, F. 31 34 38 39 45 48—50 54 56 58 71 96 105 126 133 185 202 205 219—221 236 239 259 275 287 293 344 425 441
Odlyzko, A. 378
Oldham, K.B. 284 285
Operational derivation 493
Operational techniques 218 226 228 231 234 247 258 259
Operations research 9
| Orthogonal polynomials 9 71 73 76 139 403 409 434
Orthogonality property 10 71 see
Osier, T.J. 285 287 306—308
Ossicini, A. 188 189
Panda, R. 57 61 63 65 66 78 94 174 178 179 182 193 194 258 259 278 282 386 390 400 434 437 439 454 462 475 477 481 482 484 485 488 see R."
Pandey, R.C. 70
Pandey, R.N. 258
Pandey, V.M. 258
Parabolic cylinder function 13 40
Partial fractions 480
Pasternack polynomials 9 183
Pasternack polynomials, generating function for 184
Pasternack, S. 183 184
Pathan, M.A. 78 237 238 276—278
Patil, K.R. 78 448 502
Pfaff, J.F. (1765—1825) 34
Picard, E. (1856—1941) 54 60
Pincherle, S. (1853—1936) 49
Pochhammer symbol 17 21 29 41
Pochhammer's double-loop contour integrals 70 223 228
Pochhammer, L. (1841—1920) 54
Pogorelov, V.I. 245
Poisson — Charlier polynomials 9 13 75 425 442 444
Poisson — Charlier polynomials, hypergeometric representation for 41
Polya, G. 82 354 355 377 384 385
Pontrjagin, L.S. 313
Popov, G.Ja. 181
Post, E.L. 284
Prabhakar, T.R. (1933—1982) 280 433
Pradhan, K.M. 179
Prajapat, M.L. 78 258 259 283 448
Prasad, Y.N. 258
Preiser, S. 432
Principal branch 32
Probabilistic method 10
Probability integral 17
Prym's function 17 27
Psi function 18
Quadratic transformations 33 95 96 126 189 190
Queueing theory 9
Rahman, M. 168
Rai, P.N. 416
Raina, R.K. 78 454 465 490
Rainville's method 114
Rainville, E.D. (1907—1966) 71 79 82 91—93 96 101 109 110 112 127 132 137 139 141 185 186 236 248 281 327 368 371 373 419
Rangarajan, S.K. 130 134 189 273
Rashed, T.M.T. 278
Recurrence relation 20 21 71 see
Recursion formula 27
Regular singularities 29 36
Rice polynomials 9 15
Rice polynomials, generalized 15 36
Rice polynomials, generating function for 139 146 157
Rice, S.O. 140
Riemann — Liouville fractional derivative see "fractional derivative"
Riemann, B. (1826—1866) 285
Riordan, J. 356 385
Rodrigues formula 71 241 242 408 413 see
Rodrigues O. (1794—1851) 71
Rodrigues-type representation 402
Rosenbloom, P.C. 426
Ross, B. 284
Rota, G.C. 378
Saalschuetz's theorem 95
Sack, R.A. 467
Saha, B.B. 348 416 451
Saran's notations 14 66
Saran, S. (1928—1983) 66 411 412 443
Saxena, R.K. 47 51 192 235—237
Schlaefli, L. (1814—1895) 60
Schroedinger, E. (1887—1961) 10 311
Shah, M. 454
Shanker, O. 390
Sharma's result 243
Sharma, B.L. 106 110 114 117 119 125 156 159 165 169 213—216 239 240 268 279 280 295 308 386 441 452 454
Sheffer sets 378
Sheffer, I.M. 368
Shively polynomials 9 16 187
Shively polynomials, generating function for 187
Shively, R.L. 187
Shreshtha, R.M. 94 199 367
Shrivastava, P.N. 401
Shukla, D.P. 462 493
Siddiqui, A. 258
Singh, L.S. 413
Singh, R.P. 251 252
Singh, S.D. 413 447
Singh, S.N. 413 447
Singhal — Srivastava theorem 414
Singhal, B.M. 61
Singhal, J.P. 78 82 89 90 99 157 165 171 253—255 258 259 281 375 380 381 387—390 399 401 411 412 414 430 432 451 467 468 470 496 497 499 501
Slater, L.J. 31 39 54 95 236
Slepian, D. 467
Soni, N.K. 467
Spanier, J. 284 285
Spherical polynomials see "Legendre polynomials"
Springer, M.D. 51
Srivastava — Singhal formula 432 470 473 497
Srivastava — Singhal polynomials 15 16 412 432 447
Srivastava — Singhal result 389 474
Srivastava's bilinear relations 272 443 452
Srivastava's formula 61 367
Srivastava's functions 14 15 69 119
Srivastava's generating function 93 107 145 148 283 294 366 481 490
Srivastava's result 125 143 145 150 352 359 365 366 384 480
Srivastava, A.N. 11 413 447
Srivastava, H.M. 11 47 51 52 54—57 60 61 63—66 68—70 78 82 89 90 92 94 97 98 106 107 112 117 119 130 134 138 143 145—152 155—157 160 162 163 165—167 169 173—176 180—182 192 194—198 201 214 217 221—226 228 231 232 234—238 242—244 253—259 261—266 269 271—278 281—284 304 354 358—361 368—371 373—375 380 381 383 384 386—391 394—396 398—403 407 408 411—417 421 427 429—432 434 437 438 440—447 451 452 454—468 470 471 473 475 477 481 482 484 485 488 490—497 499—502
Srivastava, R. 11 393 see R."
Stanton, D. 117
Statistics 10
Stirling numbers 16 396
Stirling's formula 23
Stochastic processes 9
Strehl, V. 467
Struve functions 15 16 44
Summability method 9
Summability method Abel's 9
Summability method Cesaro's 9
Sun, H.S. 130 189
Sylvester polynomials 9 17 185
Sylvester polynomials, generalized 17 403 450
Sylvester polynomials, generating function for 185 450
Szegoe's method 10
Szegoe, G. 41 71 82 91 135 354 355 377 388 425
Tatarskii, V.I. 245
Taylor series 475
Taylor's expansion 10 355
Taylor's theorem 82 377 379 413
Tchebycheff's method Tchebycheff polynomials 9 16 71 73 125 403 409 423
Tchebycheff's method Tchebycheff polynomials, connections between 73
Tchebycheff's method Tchebycheff polynomials, generating function for 83 423
Tchebycheff's method Tchebycheff polynomials, hypergeometric representation for 36
Tchebycheff, P.L. (1821—1894) 9
Thakare, N.K. 78 197 198 359 389 448 470 473 474 499 502
Thorne, C.J. 368
Toscano, L. 439 493
Touchard polynomials 16 184
Touchard polynomials, generating function for 184 185
Touchard, J. 184
Tremblay, R. 78 90 165 285 287 306 307
Tricomi's formula 413
Tricomi, F.G. 31 34 38 39 45 48—50 54 56 58 71 90 96 105 126 133 185 202 205 219—221 236 239 259 275 287 293 344 425 441
Truesdell's method 10
Truesdell, C. 331
Ultraspherical polynomials see "Gegenbauer polynomials"
Vandermonde's convolution theorem 31
Vandermonde, A.T. (1735—1796) 31
Varma, R.S. (1905—1970) 368
Vector space 13 311
Verma, A. 234 272 278 400
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