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Bruce C.Berndt — Ramanujan's Notebooks (part 2)
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Название: Ramanujan's Notebooks (part 2)Автор: Bruce C.Berndt Аннотация: 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.
Язык: Рубрика: Математика /Анализ /Продвинутый анализ /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1989Количество страниц: 359Добавлена в каталог: 20.10.2004Операции: Положить на полку |
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Abel — Plana summation formula 221 Abel's formula 88 Absolutely complete series 320 Achuthan, P. 126 130 Aiyar, M.V. see “Ayyar” 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 8—9 36 41 86—87 137 219 225 Asymptotic expansions 5 54—56 168 181—184 185—218 238—239 283—291 300—314 337 Atkin, A.O.L. 329 Ayoub, R. 73 283 305 Ayyar (Aiyar), M.V. 253 256 261—263 Bailey, W.N. 42 48 59 Barnes, E.W. 214 Batut, C. 162 Bauer — Muir transformation 159 162 Bauer, G. 24 145 Belevitch, V. 134 Berndt, B.C. 240 245 253 256 258—261 263 276—277 293—295 299 326 333 Bernoulli number 36 301 Bessel functions 51 58—59 133 186 214 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. 187 262 293—294 299 Chandrasekharan, K. 262 276 Character (mod 4) 240 Chowla, S. 262—263 277 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 4 103—107 112—166 168—172 175—183 Continued fractions notation 104—105 Continued fractions of Bessel functions 133 Continued fractions of gamma functions 132 140—164 Continued fractions of hypergeometric functions see “Hypergeometric functions” 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. 46—47 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 320—321 Dickson, L.E. 327 Discriminant function 326 Divisor problem 304 Divisor sums 301 313—314 319 327 329—330 Dixon, A.C. 4 7 15 22 24—25 46 60—62 Dougall, J. 8 40 47 145 Dyson — Gunson — Wilson identity 15 Edwards, J. 102 162 192 Eisenstein series 5 240 301 318—320 326—333 Elliptic integral 38 79—80 281 Endelyi, A. 44 Euler — Maclaurin summation formula 208 300—302 Euler, L. 103 106 114 129 132—133 137 141 168 185 Evans, R.J. 5—6 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 96 172—175 Gamma function, continued fractions see “Continued fractions” 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 7—9 11 15 18 20—22 24 39 41 50 57—61 63 86 102—103 145—146 156 168 181 185 190 192 214 225 240 261—262 284 293 295 298 304—305 333 Henriei, P. 221 247—248 Herschfeld, A. 109 Hill, J. 242 Hill, M.J.M. 34 Hurwitz, A. 256 262 Hypergeometric series 4 7—102 186 196 245—248 Hypergeometric series, asymptotic formulas 12—15 40—43 52 70—77 193—205 Hypergeometric series, balanced 13 48 70—77 80 Hypergeometric series, confluent 186 193—193 202—205 Hypergeometric series, continued fractions 103 112 115—117 120 131 134—137 139—140 142—145 164—165 180 Hypergeometric series, differential equations 49 87—92 Hypergeometric series, partial sums 11—14 39 41—42 45—47 Hypergeometric series, products 48 58—64 Hypergeometric series, quadratic transformations 48—51 58 64 92—99 Imperfect series 320 Inclusion-Exclusion Principle 28 Incomplete series 320 Infinite products 230—231 241 Infinite radicals 108—112 Integrals 31—32 54—56 79—80 166—171 178—182 185—207 216—217 219—227 229—237 263—264 278—279 Iseki, S. 276 Ismail, M.E.H. 6 321 323 Iteration of function 335—338 Ivic, A. 304 Iwaniec, H. 304 Jackson, D.M. 126 130 133 Jacobi, C.G.J. 9 185 Jacobsen, L. 6 104 107 109 121—124 132 137 141 146 148 156—157 159 162 164—165 169 Jogdeo, K. 182 Jones, W.B. 105 116 121—122 129 134 Jordan, W.B. 145 Kampe de Feriet, J. 8 Karlsson, P.W. 7 Katayama, K. 276—277 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 36—37 42 48—50 64 92—93 96 117 L-function 259 276—277 Lagrange inversion formula 100—102 198 202 Lagrange, J. 253 256 261 Lagrange, J.L. 133 Laguerre, E. 132 Lambert, J.H. 133 Lamm, G. 40 Lampherre, R.L. 5—6 243 Landau's constant 40 Landau, E. 304 Lavoie, J.L. 19 Lawden, D.F. 182 Lebedev, N.N. 186 193 202 Legendre polynomials 65—69 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 162 Malurkar, S.L. 256 261—263 276—277 295 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 5 314—317 Modular equation 301 333—335 338 Modular form 327—329 Morley, F. 25 Mozzochi, C.J. 304 Muir, T. 129 Multiplier for modular equation 334 Nagasaka, C. 276 Nanjundiah, T.S. 261—263 277 294 295 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. 6 104 168 184 208 212—214 216 Paris, R.B. 182 Parseval's theorem 186 207 224—225 Partial fraction decompositions 237 241 248—249 267—275 277—279 291—293 314—315 Partition function 305 Perfect series 320 Perron, O. 105—106 112 120 132—135 137 141 146 148 156 159 170 Pfaff, J.F. 9 36 93 Phillips, E.G. 294—295 Pincherle, S. 142—143 Poisson distribution 182 Poisson summation formula 5 225 233 235 238 240 252—253 264 316—317 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. 318—320 326 328 332 Rao, M.B. 253 256 261—263 Rao, S.N. 276 Razar, M.J. 276 Residue for double pole 324 Residue for triple pole 325 Riemann zeta-function 30—31 150 153 155 173 276 301 306—321 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. 256 262 293—295 Sayer, F.P. 293—295 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. 276 293—294 Srivastava, H.M. 61 St. Paul 1 Stanton, D. 7 15 48 70 77 102 Stieltjes, T.J. 141 149—151 154 156 163 Szabo, A. 40 Szegoe, G. 109 181—182 184 Terras, A. 276 Theory of indices 320 Theta-function 253 301 314 322—323 Theta-function reciprocal 305 Thomae, J. 7 39 Thron, W.J. 105 116 121—122 129 134 Titchmarsh, E.C. 189 191 223—225 235 257 289 301 304 306—307 311 317 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 36—37 Vaughn, J. 6 Venkatachaliengar, K. 319 Vijayaraghavan, T. 108—109 Vivekananda 1
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