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Bruce C.Berndt — Ramanujan's Notebooks (part 5)
Bruce C.Berndt — Ramanujan's Notebooks (part 5)



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Название: Ramanujan's Notebooks (part 5)

Автор: Bruce C.Berndt

Аннотация:

This book constitutes the fifth and final volume to establish the results claimed by the great Indian mathematician Srinivasa Ramanujan in his "Notebooks" first published in 1957. Although each of the five volumes contains many deep results, perhaps the average depth in this volume is greater than in the first four. There are several results on continued fractions a subject that Ramanujan loved very much. It is the author's wish that this volume and previous volumes will serve as springboards for further investigations by mathematicians intrigued by Ramanujan's remarkable ideas.


Язык: en

Рубрика: Математика/Анализ/Продвинутый анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 624

Добавлена в каталог: 30.10.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abel — Plana summation formula      409 411 416 419—422
Abel — Plana summation theorem      417
Adiga, C.      6 37
Aiyar, M.V.      424 435
Alladi, K.      35 49
Analogue of K(k) in signature      3 133
Ananda Rau, K.      321
Anderson, N.      6
Andrews, G.E.      2 5 6 10 37 39 46—48 50
Apostol, T.M.      566
Arithmetic-geometric mean      90
Askey, R.A.      3 6 549 558 572
Atkin, A.O.L.      136 322 455
Bachman, G.      3 6 410 491 500
Bailey's $_6{\psi}_6$ summation      138
Bailey, W.N.      73 80 106 487 506 514 573
Barrow, D.F.      490 491
Base      91
Basic hypergeometric function      43
Bauer — Muir transformation      33 37 55—57 77
Bernoulli numbers      12 66 67 410 423 425—427 444 445 466 478 488 489 513 517—519 532 580 603
Bernoulli polynomials      411
Berwick, W.E.      311 312 321
Bessel function      69 71 577
Bhargava, S.      2 6 37 133 180
Biagioli, A.J.      6
Bialek, P.      3 6 427
Birch, B.J.      258 259 322
Boas, R.P.Jr.      505
Borevich, Z.I.      224 263
Borwein, cubic theta-function      327
Borwein, cubic theta-function identity      93
Borwein, J.M.      6 89 90 93 94 97 108 111 135—137 143 152 180 187 205 281—284 324 330 334 451
Borwein, P.B.      6 89 90 93 94 97 108 111 143 152 187 205 281—284 330 334
Bowman, D.      48
Bradley, D.      3 6 27 451 547
Brent, R.      3 470 505 547 569
Brillhart, J.      188 189 276
Brychkov, Yu.A.      570 573
Buell, D.A.      225
Cardan's method      271 272
Carr, G.S.      81 208 209
Catalan's constant      458
Cauchy, A.      430 440 442 463
Chan, H.H.      1—3 6 10 20 29 30 46 50 97 180 183 186 208 259 277 317 327 336—338 341 343 346 351 362
Chandrasekharan, K.      309
Charlier polynomials      504 558
Chen, I.      322
Chrystal, G.      81
Chudnovsky, D.V.      90
Chudnovsky, G.V.      90
Class field theory      186 257—265
Class invariants      21 22 183 324
Class number      217
Clausen's formula      90 177 178
Cohen, H.      6 39 224
Complementary modulus      323
Complete elliptic integral of the first kind      90 185 323
Comtet, L.      508 509
Confluent hypergeometric function      523
Confluent hypergeometric function, of the second kind      523
Continued correspondence      68 72
Continued fractions      9—88
Continued modified convergence      35
Copson, E.T.      69
Cox, D.A.      183 258—260 262—264 309 310
Cubic analogue of the arithmetic-geometric mean      97
Cubic analogue of the Jacobian functions      133
Cubic continued fraction      208
Cubic theta-function identity      96
Cubic transformation      96 97 101 123
Davenport, H.      575
Dedekind eta-funciion      217 323
Dedekind zeta-funclion      217
Dedekind zeta-function for an ideal class      217
Degree      91
Denesting      208
Denesting theorem      284
DeTemple, D.W.      532
Deuring, M.      183 259
Dimidiation      101
Dirichlet L-function      575
Dirichlet, P.G.L.      436
Discriminant      217
Duplication      101
Eisenstein series      97 105 376—378 409 426 484
Elliptic integrals      355—356 403—405
Empirical method      205
Empirical process      184—186 257
Epstein zeta-function      216
Erdelyi      80 161 162 524
Eta-function identity      20
Euler $\varphi$-function      131
Euler constant      50 53 165 217 445 451 531 536 540 542
Euler continued fraction      77 79
Euler identity      47 49 187
Euler numbers      503 546
Euler pentagonal number theorem      92
Euler — Maclaurin summation formula      410 477 504 513 543 563 577
Euler, L.      47 81 410 439 490 496 531 532
Evans, R.J.      3 6 503 522 541 542
Faa di Bruno's formula      525
False theta-function      503 545
Farkas, H.F.      180
Ferrari's method      331
Fiedler, E.      386
Fine, N.J.      136
Fitzroy House      93
Frank, E.      79
Frankel, N.E.      549
Fundamental unit      217 317
Galway, W.      451 503 547
Gamma function      50 — 66
Garvan, F.G.      2 6 94 111 135 136 180 181
Gasper, G.      138
Gauss genus character      218
Gauss's continued fraction      76
Gauss's theorem      487
Gauss, C.F.      90
Gaussian binomial coefficient      30
Gaussian quadrature      549 558
Gelfond — Schneider theorem      165
General convergence      88
Genus field      259
Genus group      218
Gerretsen, J.      421
Gill, J.      82
Glaisher, J.W.L.      427 430
Glasser, M.L.      3 6 548 549 566
Gordon, B.      46 49 50
Goursat, E.      97
Greenhill, A.G.      281 312 313 316 321 353
Groebner bases      253
Gross, B.H.      322
Grosswald, E.      5 424
Group of units      218
Hafner, J.L.      3 6 445 476 560
Hahn polynomials      504 551
Halberstam, H.      6
Hall, H.S.      271 331 359
Hanna, M.      386 389
Hardy, G.H.      4 9 10 20 37 48 67 74 76 93 184 277 424 428 434 467 470 505 536 537
Harmonic series      531 543
Heine, E.      43
Henrici, P.      144 411
Hilbert class field      257
Hildebrand, A.      3 6 482 500
Hirschhorn, M.D.      37 46 48 135 136 180
Hua, L.K.      442
Huang, S.-S.      36 50 183 259
Huard, J.G.      324
Hurwitz zeta-function      513
Hurwitz, A.      427
Hypergeometric functions      72 73 89 90 323 327—328 503 566 572
Ideal class character      217
Ideal class group      217
Incomplete gamma function      524
Infinite exponential      410 490
Institute for Advanced Study      5
Inversion formula      92 93 99
Iterated logarithm      491
J-invariant      186
Jacobi triple product identity      323
Jacobi's identity for fourth powers      93
Jacobi, C.G.J.      377
Jacobsen, L.      2 12 33 35 38 51 62 65 72 85 88
Janusz, J.      262
Jones, W.B.      12 34 68 70 72 81 85—88
Jordan, C.      514
Joshi, P.      6
Journal of the Indian mathematical society      440 461
Joyce, G.S.      324 327
K-periodic continued fraction      81 83 84
Kaltofen, E.      322
Kaplan, P.      324
Kaufmann-Buhler, W.      6
Keckic, J.D.      66
Khovanskii, A.N.      68 83
Knight, S.R.      271 331 359
Knoebel, A.      490
Knopp, M.I.      5 130
Kopeliovich, Y.      180
Kortum, R.      225
Kowalenko, V.      549
Kra, I.      180
Krishnaiah, P.V.      467
Kronecker limit formula      341
Kronecker's Limit Formula      216—243
Kronecker, L.      218
Lagrange inversion formula      490
Laguerre polynomial      524
Lambert series      373—376 504
Lambert, J.H.      70
Lamphere, R.L.      2 6
Landau, S.      284
Landen's transformation      101
Lebedev, N.N.      523
Legendre, A.M.      302
Lewin, L.      40
Limit k-periodic continued fraction      81 85
Limit periodic continued fraction      82
Lindemann, L.      6
Littlewood, J.E.      467 470
Logarithmic integral      542
Lorentzen, L.      6
Lost notebook      10 36 37 39 41 48 50
Macsyma      515 517 520—522 542
Maple      96 144 174 175 180
Marichev, O.I.      570 573
Mathematica      129 131 132 145 179 254 255 257 269 270 301 310 315 316 335 336 343 369 383 384 393—395 397 406 469 532 541 547 555 560 564 577
Mclntosh, R.      6
McNiel, G.      225
Method of successive approximations      541
Meyer, J.      383 393
Mitrinovic, D.S.      566
Modified hypergeometric function      549
Modified theta-function      549
Modular equations      49 91 92 94 185 243—257 324 353—407
Modular equations in the theory of signature 3      120—133
Modular equations of degree      120
Modular equations of degree 11      125—129 155—156 372
Modular equations of degree 13      159—160 387
Modular equations of degree 14      128—132
Modular equations of degree 15      385
Modular equations of degree 16      368
Modular equations of degree 17      388
Modular equations of degree 19      386
Modular equations of degree 20      128—132
Modular equations of degree 21      380
Modular equations of degree 25      160—161 396
Modular equations of degree 27      386 394
Modular equations of degree 29      388
Modular equations of degree 3      121—124 153—154 156—157 222 302 354—363
Modular equations of degree 31      385
Modular equations of degree 33      380 392
Modular equations of degree 35      380 381 386 392
Modular equations of degree 37      388
Modular equations of degree 39      381
Modular equations of degree 47      385
Modular equations of degree 49      396 397
Modular equations of degree 5      124—126 154—155 157—158 223 303 363—367
Modular equations of degree 51      392
Modular equations of degree 55      380 392
Modular equations of degree 59      386
Modular equations of degree 65      381
Modular equations of degree 7      125 155 158 223 368 369
Modular equations of degree 71      385
Modular equations of degree 8      128—133 368
Modular equations of degree 9      123—125 158 370—372 387 394
Modular equations of degree 95      385
Modular equations of degree n      185
Modular equations of Weber type      132
Modular j-invariant      309—322
Modulus      89 90 183 323
Moebius function      409 467
Mollin, R.      219 222
Montgomery, H.L.      428 436
Mordell, L.J.      89
Morton, P.      188 189 276
Multiplier      13 91 92 324
National Science Foundation      6
National Security Agency      6
Nielsen, N.      542
Nikiforov, A.F.      551 558
Niven, I.      428 436
Nome      91
Norm      209
Norm of an ideal      217
Olver, F.W.J.      410 425 516 523 526 534 543 569
Orthogonal polynomials      557 558
Pentagonal number theorem      131 132
Perimeter of ellipse      541
Perron, O.      37 58 76 81—83
Pfaff's transformation      302 572
Pohst, M.      225
Poisson distribution      558
Poisson summation formula      409 447 466 467
Poisson summation formula for Fourier sine transforms      449 576
Preece, C.T.      73 74 76 424
Princeton University      5
Principal genus      218
Prudnikov, A.P.      570 573
Purtilo, J.M.      6
q-continued fractions      45—50
Quintuple product identity      18
Rademacher, H.      548
Rahman, M.      138
Ramanathan, K.G.      10 20 22 44 46 48—50 76 204 220 221 277 281—284 339 354 379 386
Ramanujan's cubic continued fraction      28
Ramanujan's cubic transformation      93 332
Ramanujan's quarterly reports      562
Rankin, R.A.      5 128 172 321 382 429 455 603
Rao, M.B.      424 435
Representations of n as a sum of four squares      377
Riemann functional equation      410
Riemann hypothesis      470
Riemann zeta-function      56 218 410 423 471 472 476 477 503 534 540
Riordan, J.      525
Rising factorial      411
Rogers — Ramanujan continued fraction      9 10 12—45
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