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Bruce C.Berndt Ч Ramanujan's Notebooks (part 2)
Bruce C.Berndt Ч Ramanujan's Notebooks (part 2)

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Ќазвание: Ramanujan's Notebooks (part 2)

јвтор: Bruce C.Berndt

јннотаци€:

During the years 1903-1914, Ramanujan recorded many of his mathematical discoveries in notebooks without providing proofs. Although many of his results were already in the literature, more were not. Almost a decade after Ramanujan's death in 1920, GN Watson and BM Wilson began to edit his notebooks, but never completed the task. A Photostat edition, with no editing, was published by the Tata Institute of Fundamental Research in Bombay in 1957.
This book is the second of four volumes devoted to the editing of Ramanujan's Notebooks. Part I, published in 1985, contains an account of Chapters 1-9 in the second notebook as well as a description of Ramamnujan's second notebook. If a result is known, we provide references in the literature where proofs may be found; if a result is not known, we attempt to prove it.

Not only are the results fascinating, but, for the most part, Ramanujan's methods remain a mystery. Much work still needs to be done. We hope readers will strive to discover Ramanujan's thoughts and further develop his beautiful ideas.


язык: en

–убрика: ћатематика/јнализ/ѕродвинутый анализ/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1989

 оличество страниц: 359

ƒобавлена в каталог: 20.10.2004

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Abel Ч Plana summation formula      221
Abel's formula      88
Absolutely complete series      320
Achuthan, P.      126 130
Aiyar, M.V.      see УAyyarФ
Aiyar, S.N.      285
Allen, E.J.      109
Andoyer, H.      137
Andrews, G.E.      1 6 15 127 305
Apery, R.      155 162
Apostol, T.M.      259 276 330
Appell, P.E.      8
Appledorn, C.R.      216
Askey, R.A.      6 8Ч9 36 41 86Ч87 137 219 225
Asymptotic expansions      5 54Ч56 168 181Ч184 185Ч218 238Ч239 283Ч291 300Ч314 337
Atkin, A.O.L.      329
Ayoub, R.      73 283 305
Ayyar (Aiyar), M.V.      253 256 261Ч263
Bailey, W.N.      42 48 59
Barnes, E.W.      214
Batut, C.      162
Bauer Ч Muir transformation      159 162
Bauer, G.      24 145
Belevitch, V.      134
Berndt, B.C.      240 245 253 256 258Ч261 263 276Ч277 293Ч295 299 326 333
Bernoulli number      36 301
Bessel functions      51 58Ч59 133 186 214
Binet, J.      206 221
Binomial coefficient identities      69
Birthday surprise problem      182
Blaum, M.      182
Boas, R.P.      226
Bodendiek, R.      276
Boersma, J.      294
Bowman, K.O.      181
Bromwich, T.J.PA.      238
Brouncker, Lord      145
Bruckman, P.S.      299
Buckholtz, J.D.      182
Buehler, W.K.      8
Buehring, W.      77
Burkhardt, H.      206
C-fraction      175
Carlitz, L.      182
Carlson, B.C.      15
Carr, G.S.      102 134
Catalan's constant      40 45 151 153
Cauchy, A.      187 262 293Ч294 299
Chandrasekharan, K.      262 276
Character (mod 4)      240
Chowla, S.      262Ч263 277
Chrystal, G.      106
Churchill, R.V.      324
Clausen, T.      58
Coddington, E.A.      88
Cohen, H.      6 151 162 175
Complete series      320
Continued fractions      4 103Ч107 112Ч166 168Ч172 175Ч183
Continued fractions notation      104Ч105
Continued fractions of Bessel functions      133
Continued fractions of gamma functions      132 140Ч164
Continued fractions of hypergeometric functions      see УHypergeometric functionsФ
Continued fractions periodic      116
Continued fractions tails      105 107 112 115 119 120
Continued fractions, even part      121
Continued fractions, general convergence      123
Continued fractions, kth numerator and denominator      105
Copson, E.T.      34 66 182 203 307
Coulomb approximation      40
Darling, H.B.C.      46Ч47
De Morgan, A.      127 129
de Saint-Venant, M.      294
Dedekind eta-function      253 281 305
Dedekind zeta-function      276
Degree of a modular equation      334
Degree of a series      320Ч321
Dickson, L.E.      327
Discriminant function      326
Divisor problem      304
Divisor sums      301 313Ч314 319 327 329Ч330
Dixon, A.C.      4 7 15 22 24Ч25 46 60Ч62
Dougall, J.      8 40 47 145
Dyson Ч Gunson Ч Wilson identity      15
Edwards, J.      102 162 192
Eisenstein series      5 240 301 318Ч320 326Ч333
Elliptic integral      38 79Ч80 281
Endelyi, A.      44
Euler Ч Maclaurin summation formula      208 300Ч302
Euler, L.      103 106 114 129 132Ч133 137 141 168 185
Evans, R.J.      5Ч6 12 40 48 65 70 77 186 202 216 243
Exponential integral      184
Exponential series      181
Fichtengolz, G.M.      232
Fields, J.      6 12
Flajolet, P.      6 130 300
Fletcher, A.      96
Frasch, H.      328
Frullani's theorem      162
Gamma function      5 96 172Ч175
Gamma function, continued fractions      see УContinued fractionsФ
Gamma function, logarithmic derivative      8 43 104
Gauss's continued fraction      103 134
Gauss's theorem      17 25 26 36 56 84 120
Gauss, C.F.      4 7 34 36 42 50 57 92
Generalized hypergeometric series      8
Gessel, I.      7 15
Glaeske, H.J.      276
Glaisher, J.W.L.      192 262 315 327
Glasser, M.L.      6 226
Goldberg, L.      305
Goldstein, L.J.      276
Gosper, R.W.      7
Gould, H.W.      69
Gouldlen, I.P.      126 130
Graham, S.      304
Grosjean, C.C.      294 329
Grosswald, E.      256 261 276
Guinand, A.P.      256 262 276
Hafner, J.L.      304
Halbritter, U.      276
Halphen, M.      327
Hansen, E.R.      69
Hardy, G.H.      2 4 7Ч9 11 15 18 20Ч22 24 39 41 50 57Ч61 63 86 102Ч103 145Ч146 156 168 181 185 190 192 214 225 240 261Ч262 284 293 295 298 304Ч305 333
Henriei, P.      221 247Ч248
Herschfeld, A.      109
Hill, J.      242
Hill, M.J.M.      34
Hurwitz, A.      256 262
Hypergeometric series      4 7Ч102 186 196 245Ч248
Hypergeometric series, asymptotic formulas      12Ч15 40Ч43 52 70Ч77 193Ч205
Hypergeometric series, balanced      13 48 70Ч77 80
Hypergeometric series, confluent      186 193Ч193 202Ч205
Hypergeometric series, continued fractions      103 112 115Ч117 120 131 134Ч137 139Ч140 142Ч145 164Ч165 180
Hypergeometric series, differential equations      49 87Ч92
Hypergeometric series, partial sums      11Ч14 39 41Ч42 45Ч47
Hypergeometric series, products      48 58Ч64
Hypergeometric series, quadratic transformations      48Ч51 58 64 92Ч99
Imperfect series      320
Inclusion-Exclusion Principle      28
Incomplete series      320
Infinite products      230Ч231 241
Infinite radicals      108Ч112
Integrals      31Ч32 54Ч56 79Ч80 166Ч171 178Ч182 185Ч207 216Ч217 219Ч227 229Ч237 263Ч264 278Ч279
Iseki, S.      276
Ismail, M.E.H.      6 321 323
Iteration of function      335Ч338
Ivic, A.      304
Iwaniec, H.      304
Jackson, D.M.      126 130 133
Jacobi, C.G.J.      9 185
Jacobsen, L.      6 104 107 109 121Ч124 132 137 141 146 148 156Ч157 159 162 164Ч165 169
Jogdeo, K.      182
Jones, W.B.      105 116 121Ч122 129 134
Jordan, W.B.      145
Kampe de Feriet, J.      8
Karlsson, P.W.      7
Katayama, K.      276Ч277
Khovanskii, A.N.      105 134 170
Kirschenhofer, P.      276
Klamkin, M.S.      182
Klein, F.I.      8
Klusch, D.      299
Knopp, K.      268
Knuth, D.E.      182
Kolesnik, G.      304
Koshliakov, N.S.      262
Krischnamachari, C.      256 262
Krishnan, K.S.      226
Kummer's theorem      17 21 24
Kummer, E.E.      4 7 36Ч37 42 48Ч50 64 92Ч93 96 117
L-function      259 276Ч277
Lagrange inversion formula      100Ч102 198 202
Lagrange, J.      253 256 261
Lagrange, J.L.      133
Laguerre, E.      132
Lambert, J.H.      133
Lamm, G.      40
Lampherre, R.L.      5Ч6 243
Landau's constant      40
Landau, E.      304
Lavoie, J.L.      19
Lawden, D.F.      182
Lebedev, N.N.      186 193 202
Legendre polynomials      65Ч69
Legendre, A.M.      165
Lehmer, D.H.      330
Lerch zeta-function      259
Lerch, M.      276 293
LeVeque, W.J.      330
Levitt, J.      329
Lewittes, J.      256
Lindeloef, E.      221
Linear series      321
Ling, C.-B.      256 262 299
Littlewood, J.E.      305
MacMahon, P.A.      28
Madhava, K.B.      150
Malmsten's integral representation of $\mathrm{Log}\,\Gamma(z)$      162
Malurkar, S.L.      256 261Ч263 276Ч277 295
Marsaglia, J.C.W.      181
Masser, D.W.      6 329
Masson, D.      141 142 145
Matala-Aho, T.      38
Mathematical gazette      182 295
Matsuoka, Y.      276
McCabe, J.H.      130
McKay, J.H.      108
Mellin, H.      295
Mikolas, M.      276
Mixed series      320
Modified theta-function      5 314Ч317
Modular equation      301 333Ч335 338
Modular form      327Ч329
Morley, F.      25
Mozzochi, C.J.      304
Muir, T.      129
Multiplier for modular equation      334
Nagasaka, C.      276
Nanjundiah, T.S.      261Ч263 277 294 295
Narasimhan, R.      262 276
Newman, D.J.      182
Newton, I.      28
Nielsen, N.      32 165 181 184 206
Noerlund, N.E.      135 156
Ogg, A.      320
Olivier, M.      162
Olver, F.W.J.      6 104 168 184 208 212Ч214 216
Paris, R.B.      182
Parseval's theorem      186 207 224Ч225
Partial fraction decompositions      237 241 248Ч249 267Ч275 277Ч279 291Ч293 314Ч315
Partition function      305
Perfect series      320
Perron, O.      105Ч106 112 120 132Ч135 137 141 146 148 156 159 170
Pfaff, J.F.      9 36 93
Phillips, E.G.      294Ч295
Pincherle, S.      142Ч143
Poisson distribution      182
Poisson summation formula      5 225 233 235 238 240 252Ч253 264 316Ч317
Poisson summation formula for sine transforms      236 257 265 289
Pollak, H.O.      217
Pollard, H.      226
Ponnuswamy, S.      126 130
Preece, C.T.      121 146 156 293 295
PRIMES      304
Prodinger, H.      276
Pure series      320
Putnam, William Lowell      108
Rademacher, H.      305
Ramamani, V.      329
Ramanathan, K.G.      134 137 141 146
Rankin, R.A.      318Ч320 326 328 332
Rao, M.B.      253 256 261Ч263
Rao, S.N.      276
Razar, M.J.      276
Residue for double pole      324
Residue for triple pole      325
Riemann zeta-function      30Ч31 150 153 155 173 276 301 306Ч321
Riesel, H.      262 276 295 305
Riordan, J.      34
Rogers, L.J.      11 121 125 127 129 148 150 151 163
Roy, R.      7 225
Saalschuetz, L.      4 7 9 15 99 187
Samuels, S.M.      182
Sandham, H.F.      256 262 293Ч295
Sayer, F.P.      293Ч295
Schlaefli, L.      59
Schloemlich, O.      253 256
Schoeneberg, B.      320
Self-repeating series      336
Serre, J.-P.      320
Shepp, L.      217
Sitaramachandrarao, R.      6 256 261 271 276 293 297
Sizer, W.S.      109
Slater, L.      8
Smart, J.R.      276 293Ч294
Srivastava, H.M.      61
St. Paul      1
Stanton, D.      7 15 48 70 77 102
Stieltjes, T.J.      141 149Ч151 154 156 163
Szabo, A.      40
Szegoe, G.      109 181Ч182 184
Terras, A.      276
Theory of indices      320
Theta-function      253 301 314 322Ч323
Theta-function reciprocal      305
Thomae, J.      7 39
Thron, W.J.      105 116 121Ч122 129 134
Titchmarsh, E.C.      189 191 223Ч225 235 257 289 301 304 306Ч307 311 317
Toyoizumi, M.      276
Tricomi, F.G.      44
Trinity College      5
Tschebyscheff polynomials      99
Tschebyscheff, P.      169
University of Illinois      1
Vaeaenaenen, K.      38
Vandermonde's theorem      36Ч37
Vaughn, J.      6
Venkatachaliengar, K.      319
Vijayaraghavan, T.      108Ч109
Vivekananda      1
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