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Andrews G.E., Askey R., Roy R. — Special functions
Andrews G.E., Askey R., Roy R. — Special functions

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Название: Special functions

Авторы: Andrews G.E., Askey R., Roy R.

Аннотация:

Special functions, which include the trigonometric functions, have been used for centuries. Their role in the solution of differential equations was exploited by Newton and Leibniz, and the subject of special functions has been in continuous development ever since. In just the past thirty years several new special functions and applications have been discovered. This treatise presents an overview of the area of special functions, focusing primarily on the hypergeometric functions and the associated hypergeometric series. It includes both important historical results and recent developments and shows how these arise from several areas of mathematics and mathematical physics. Particular emphasis is placed on formulas that can be used in computation. The book begins with a thorough treatment of the gamma and beta functions that are essential to understanding hypergeometric functions. Later chapters discuss Bessel functions, orthogonal polynomials and transformations, the Selberg integral and its applications, spherical harmonics, q-series, partitions, and Bailey chains. This clear, authoritative work will be a lasting reference for students and researchers in number theory, algebra, combinatorics, differential equations, applied mathematics, mathematical computing, and mathematical physics.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 680

Добавлена в каталог: 08.12.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abel summability      599
Abel, N.H.      14 106 600 605
Absolutely monotonic series      389
Adams, J.C.      320
Adjacency matrix      266
Agarwal, R.P.      586
Ahern, P.      36
Airy, G.B.      201
Al-Salam, W.A.      532
Amend, B.      61
Anastassiadis, J.      36
Anderson, G.W.      401 402 411 430
Andrews, G.E.      171 175 574 590 592
Anno, M.      450
Aomoto, K.      401 402 406 407 428 440
Apery, R.      355
Archimedes      485
Arithmetic-geometric mean      134
Artin, E.      34 36 53
Askey, R.A.      67 185 314 322 363 369 391 394 505 519 575 592
Associated Legendre function      456
Asymptotic expansion      611
Auslander, L.      43
Azor, R.      328
Baernstein, A.      355
Bailey chain      586
Bailey pair      586
Bailey's $_{9}F_{8}$ transformation      182
Bailey's lemma      584
Bailey, W.N.      93 124 143 144 147 150 152 154 170 173 174 181 182 184 185 277 319 386 398 400
Bak, J.      306
Barnes's beta integral      90
Barnes, E.W.      61
Basic hypergeometric series      523
Basic hypergeometric series, k-balanced      524
Basic hypergeometric series, well-poised      524
Bateman, H.      277 313 314 475
Baxter, R.J.      xv
Bellman, R.      535 542
Berggren, L.      139
Berndt, B.      532 627
Bernoulli numbers      12
Bernoulli polynomials      20 615
Bernoulli polynomials, generalized      615
Bernoulli, D.      2
Bernoulli, J.      605 615 619
Bessel functions      200 204—206 212
Bessel functions, Bessel's formula      212
Bessel functions, Gegenbauer's formula      205
Bessel functions, generating function      212
Bessel functions, Hankel's formula      206
Bessel functions, Poisson integral      204
Bessel functions, second kind      200
Bessel's equation      200
Bessel's inequality      264
Bessel, F.W.      187 200 202 203 222 225 228 230 231 288 321 464 475
Beta integral      4
Beukers, F.      355
Bieberbach, L.      355 362 382
Binet, J.P.M.      28 29
Boas, R.P.      410
Bochner, S.      464 542
Bohr, H.      363 494
Borel, E.      608
Borwein, J.      139
Borwein, P.      139
Brafman, E      400
Brent, R.P.      138
Bressoud, D.M.      401 429 590 591
Bromwich, T.J.      630
Brown, G.      376
Brown, M.      552
Brualdi, R.A.      371
Burge, W.H.      171
Bustoz, J.      608
Butlewski, Z.      238
Caratheodory, C.      49
Carlson's theorem      110
Carlson, F.      109
Cartier, P.      371
Cauchy, A.L.      263 442 491 497 523 541 542 548
Cayley, A.      268
Cesaro summability      599
Cesaro, E.      355 599 604 605
Characters      38 57
Characters, additive      38
Characters, even      58
Characters, multiplicative      38
Characters, odd      58
Characters, primitive      79
Charlier polynomials      347
Charlier, C.V.L.      349
Chebyshev polynomials      101 102
Chebyshev polynomials, first kind      101
Chebyshev polynomials, fourth kind      102
Chebyshev polynomials, second kind      101
Chebyshev polynomials, third kind      102
Chebyshev, P.L.      117
Christoffel, E.B.      240 261 272 373
Christoflel — Darboux formula      246
Chu — Vandermonde identity      67
Chu, S.-C.      67
Clausen's identity      116
Clausen, T.      116
Confluent hypergeometric equation      188 190 194
Confluent hypergeometric equation, asymptotic solutions      190
Confluent hypergeometric equation, recessive solutions      194
Connor, W.G.      576
Contiguous $_{4}F_{3}$      155
Cooley, J.W.      43
Cooper, S.      409
Copson, E.T.      463
Cosine integral      235
Coulomb wave function      199
Cox, D.      134
Darboux's method      310
Darboux, J.G.      240 243 271 272
Davenport, H.      430 432
de Boor, C.      43
de Branges, L.      152 355 382 520
de Bruin, N.G.      234 282
de Moivre, A.      18
Dedekind $\eta$-function      538
Dedekind, R.      1
DeSainte-Catherine, M.      330
Digamma function      13
Dilogarithm      102
Din, A.M.      322
Dirichlet L-function      58 59
Dirichlet L-function, functional equation      60
Dirichlet problem      463
Dirichlet, P.L.      1 2 401 413 434 463 532 601
Discriminant      418
Dixon, A.C.      72 239
Dougall's $_{7}F_{6}$ formula      147 152
Dougall's $_{7}F_{6}$ formula, Bailey's $_{7}F_{6}$ integral analog      152
Dougall's bilateral sum      110
Dougall's identity      71
Dougall, J.      71 143 147 182 183
Durfee, W.P.      567
Dwork, B.      46
Dyson's integral      426
Dyson, F.J.      410 426 427 590
Edwards, A.W.F.      243 485
Edwards, C.H.      485
Eisenstein, F.G.M.      12 42
Elliot, E.B.      138
Elliptic functions      508
Elliptic integrals      132 136
Elliptic integrals, first kind      132
Elliptic integrals, second kind      136
Erdelyi's formula      113
Erdelyi, A.      68 111 615
Error function      196
Euler — Maclaurin summation formula      18
Euler's angles      469
Euler's reflection formula      9
Euler's transformation      69
Euler, L.      1 2 4 469 471 490 493 497 501 508 521 523 524 553 564 627
Eulerian integral      6
Eulerian integral, first kind      6
Eulerian integral, second kind      6
Evans, R.      415
Favard, J.      245 248
Fejer, L.      269 272 313 334 355 371 372 388 602
Feldheim, E.      278 291 315 382 390
Fermat measure      486
Fermat, P.      1 485 486
Ferrers, N.M.      320 565 566
Fields, J.L.      615
Fine, N.J.      506
Finite-dimensional representation of a group      466 467 469
Finite-dimensional representation of a group, irreducible representation      469
Finite-dimensional representation of a group, isomorphism of      467
Finite-dimensional representation of a group, subrepresentation      469
Finite-dimensional representation of a group, unitary representation      467
Foata, D.      371
Forrester, P.J.      426 441
Fourier, J.      445 464 466 540 600 602 623
Fractional integral      605
Fractional integration      111
Fresnel integrals      235
Friedrichs, K.      365
Funk — Hecke formula      459
Funk, R      445 458
Fuss, N.      2
Gamma function      3 6 23 44
Gamma function, Gauss's multiplication formula      23
Gamma function, integral representation      6
Gamma function, p-adic      44
Gamma function, product representation      3
Gasper, G.      355 363 369 382 390 523 530 545
Gauss quardrature formula      250
Gauss sums      38 627
Gauss sums, reciprocity      627
Gauss's summation formula      67 90
Gauss's summation formula, integral analog      90
Gauss, C.F.      1 61 63 61 78 94 95 240 254 262 355 411 431 491 496 497 499 500 508 521 523
Gautschi, W.      212
Gegenbauer polynomials      302
Gegenbauer's addition formula      215
Gegenbauer's product formula      478
Gegenbauer, L.      187 204 302 316 318 334 464 475 478
Gelfond, A.      410
Gessel, I.      630
Gibbs phenomenon      372
Gillis, J.      328
Godsil, C.D.      266 277 328
Goldbach, C.      2
Good, I.J.      371 427 630
Gordon, B.      576
Gosper's algorithm      163
Gosper, R.W.      116
Gould, H.W.      186
Graf's formula      215
Graf, J.H.      239 475
Gram, J.-P.      277
Gray, J.      84
Gronwall, T.H.      372 380
Gross, B.      45
Guo, D.R.      29
Hahn polynomials      331 345 346
Hahn polynomials, continuous      331
Hahn polynomials, continuous dual      331
Hahn polynomials, dual Hahn      346
Hahn, W.      331 332
Halmos, P.      468
Hamburger, H.      536
Hamilton, W.R.      268
Hankel functions      208
Hankel pair      216 290
Hankel transforms      216 289
Hankel, H.      121 289—291
Hardy, G.H.      363 410 532 572 578 608
Harmonic polynomial      446
Harr measure      468
Hasse — Davenport relation      432
Hasse, H.      430 432 436
Hecke, E.      445 458
Heine's transformation formula      520
Heine, E.      274 491 520—523
Heisenberg, W.      282
Helversen-Pasotto, A.      93
Herglotz, G.      1
Hermite polynomials      278—280 318 419
Hermite polynomials, discriminant      419
Hermite polynomials, generating function      279
Hermite polynomials, linearization formula      318
Hermite polynomials, orthogonality      278
Hermite polynomials, Poisson kernel      280
Hermite, C.      100 198 266 269 271 273 299 531
Hewitt, E.      306 376
Hickerson, D.      590
Hill, M.J.M.      63
Hille, E.      226 496
Hoelder, O.      647
Hsu, L.C.      186
Hsue, H.-Y.      321
Hurwitz zeta function      15
Hurwitz, A.      1 226
Hylleraas, E.      322
Hypergeometric differential equation      75
Hypergeometric functions      64 65 87 88 94 97 125 130
Hypergeometric functions, asymptotic expansion      88
Hypergeometric functions, Barnes's integral      87
Hypergeometric functions, contiguous relations      94
Hypergeometric functions, continued fraction      97
Hypergeometric functions, cubic transformations      130
Hypergeometric functions, integral representation      65
Hypergeometric functions, quadratic transformations      125
Hypergeometric series      61 70 140 146
Hypergeometric series, balanced      70
Hypergeometric series, k-balanced      140
Hypergeometric series, nearly poised      140
Hypergeometric series, very well poised      146
Hypergeometric series, well-poised      140
Hypergeometric term      163
Incomplete gamma function      197
Ingham, A.E.      394
Ireland, K.      432
Ismail, M.E.H.      363 370 504 532 552
Ivory, J.      99
Jackson's formula      587
Jackson, D.      372 375 380
Jackson, E.H.      485 486 588
Jacobi elliptic functions      510
Jacobi polynomials      99 298 475 476
Jacobi polynomials, generating function      298
Jacobi polynomials, Koornwinder's product formula      476
Jacobi polynomials, Laplace-type integral      475
Jacobi polynomials, Poisson kernel      385
Jacobi sums      39
Jacobi, C.G.      240 277 297 298 401 411 485 496 500 501 508—510 548 591 592
Jensen, J.L.W.V.      14
Jimbo, M.      xv
John, F.      544
Johnson, W.      542 630
Jordan, C.      623
Karamata, J.      609
Karlin, S.      396
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