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Bruce C.Berndt Ч Ramanujan's Notebooks (part 3)
Bruce C.Berndt Ч Ramanujan's Notebooks (part 3)



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Ќазвание: Ramanujan's Notebooks (part 3)

јвтор: Bruce C.Berndt

язык: en

–убрика: ћатематика/јнализ/ѕродвинутый анализ/

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

ed2k: ed2k stats

√од издани€: 1991

 оличество страниц: 510

ƒобавлена в каталог: 20.10.2004

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$F(x)$      91
Adiga, C.      7 18 24 28 32 39 49 73 79 86 115 142
Agarwal, A.K.      78
Al-Salam, W.A.      79
Alder, H.L.      78
Almkvist, G.      10 147 149Ч150 456
Andrews, G.E.      10 13Ч15 18 28Ч29 32 36Ч37 77Ч80 83 347 398
Askey, R.      2 10 14 29 32 77Ч79 149
Atkin, A.O.L.      83
Ayyar, M.V.      140
Bailey, D.H.      6
Bailey, W.N.      15Ч17 83 89 111 120 181 262
Base (of an elliptic function)      5 102
Basic hypergeometric series      12
Baxter, R.J.      78
Berndt, A.      2 5 7 24 29 44 79 111Ч112 140Ч141 147 150 172 197 326 456
Bernoulli numbers      42 61Ч64 97
Berry, A.      440
Bhagirathi, N.A.      28
Bhargava, S.      7 10 18 24 28 32 39 49 73 79 115 142
Biagioli, A.J.      7 10 326 346
Blecksmith, R.      73 83
Borwein, J.M.      6 78 269 305 346 355 456
Borwein, P.B.      6 78 269 305 346 355 456
Bressoud, D.      78 398
Brillhart, J.      10 83
Brouncker, Lord      200
Burnside, W.      240
Byrd, P.F.      113
Carlitz, L.      18 79 83
Catalan's constant      154Ч155
Cauchy, A.      14 140
Cayley, A.      2Ч3 5 106Ч107 135 138 218 220 232 241
Change of sign      126 130 132 178
Chudnovsky, D.V.      168
Chudnovsky, G.V.      168
Churchhouse, R.F.      79
Clausen transformation      114
Cohn, H.      6
Column-row method of summation      114
Complementary modulus      4 102
Complete series      42 455
Consistency condition      327
Continued fraction, geometric and arithmetic mean arguments      164
Continued fractions      19Ч29 92 146 151 163Ч168 185Ч187 206Ч208 221Ч222 345Ч347
Cosine identity      345 347Ч348
Court, N.A.      245
Coxeter, H.S.M.      245
Cusp      328
Cusp parameter      328
Darling, H.A.      261
Dedekind eta-function      37 44 330Ч338
Degree of a modular equation      4
Degree of a modulus      229
Degree of series      42
Denis, R.Y.      28 78Ч79
Deutsch, J.      6
Dickson, L.E.      197 200
Digby, K.      200
Dimidiation      126 178
Diophantine equations      197Ч200
Divisor functions      62 64Ч65
Duplication      125 127Ч128 178
Dyson, F.J.      10 83
Eccentricity of an ellipse      145
Ehrenpreis, L.      78
Eisenstein series      7 65 121Ч122 126Ч139 144Ч145 175Ч177 454Ч488
Eisenstein series, values in terms of elliptic function parameters      126Ч129
Eisenstein, G.      28
Ellipse, approximations to the perimeter of      145Ч150 180Ч189
Elliptic curve      6
Elliptic functions      2Ч3
Elliptic functions, notation      101Ч102
Elliptic integral of the first kind      4 102
Elliptic integral of the second kind      176Ч177 303Ч304
Elliptic integrals      104Ч113 238Ч243 297Ч298
Elliptic integrals, addition theorem for elliptic integrals of the first kind      106Ч108
Elliptic integrals, addition theorem for elliptic integrals of the second kind      303
Elliptic integrals, duplication formula      106
Enneper, A.      5 72 220
Euler numbers      61 63
Euler's diophantine equation      197Ч199
Euler's partition theorem      37
Euler's pentagonal number theorem      36Ч37
Euler, L.      14 37 147 150 196Ч197 199
Evans, R.J.      7 83 274 276 337 352 373 375
Fergestad, J.B.      146
Fermat, P.      200
Fiedler, E.      5 315 364 416 444
Fine, N.J.      32
Fixed point of a modular form      328
Flajolet, P.      80
Forrester, P.J.      78
Forsyth, A.R.      242
Francon, J.      168
Frenicle      200
Fricke involution      216 404
Fricke, R.      5 83 364 416
Friedman, M.D.      113
Frobenius, G.      1
Fundamental set      328
Garsia, A.M.      78
Gauss' transformation      113
Gauss, A.F.      14 28 36 89 147 151 181
Geometrical problems      190Ч196 211Ч213 243Ч249 298Ч302
Gerst, I.      73 83
Ghosh, S.      488
Glaisher, J.W.L.      169 242 303
Glasser, M.L.      80 110 113
Gordon, B.      78Ч79 83 347
Gosper, R.W.      13
Gray, J.J.      28
Greenhill, A.G.      2 400 439
Guetzlaff, C.      5
Gustafson, R.      32
Hahn, W.      32
Halphen, M.      62
Hancock, H.      212
Hanna, M.      5 440 444
Hard hexagon model      78
Hardy, G.H.      2 6 9 11 29Ч32 36 39 45 77 79 84 86 126 162Ч164 197 199 262 326 346 385 426 450
Hecke operator      373
Hecke, E.      398
Heine's continued fraction      21
Heine, E.      11 14Ч15 18 21
Hermite, C.      135
Hirschhorn, M.      11 28 31 79 83 347
Hoppe, R.      196
Hovstad, R.M.      79
Hurwitz, A.      5 444
Hyperbola, perimeter of      180
Hyperbolic function series evaluations in closed form      140Ч141 157Ч162
Hyperbolic function series evaluations in terms of elliptic function parameters      132Ч139 153Ч157 172Ч178
Hyperbolic function series identity      162
Hypergeometric differential equation      120Ч121
Hypergeometric functions      3 5 88Ч104 120Ч122 144Ч150 153Ч155 185Ч186 213 238Ч239 289Ч290 455Ч456
Invariant order of a modular form      328
Inversion formula for base q      100
Ismail, M.E.H.      32 42 79
Ivory, J.      146Ч147
Jackson, F.H.      14Ч15
Jackson, M.      32
Jacobi triple product identity      11Ч12 32 35Ч36
Jacobi's identity      39
Jacobi's imaginary transformation      106 154
Jacobi, C.G.J.      3 5 11 14 36 39 54 87 115Ч116 123 126 135 143 165Ч166 169 173 176Ч177 207 218 220 232 234 239Ч241
Jacobian elliptic functions      3 54 87 107Ч108 135Ч136 138Ч139 143 162Ч163 165Ч180 207Ч208 227 242 304
Jacobian elliptic functions, conversions of old formulas into new formulas      173Ч174
Jacobsen, L.      10 20 22Ч24 26Ч27 79 84 146
Jain, V.K.      78
Journal of the Indian mathematical society      9 11 77 190 246
Joyce, G.S.      6
Kac, V.G.      398
Kepler, J.      147 150
Kiper, A.      169
Kleiber, J.      89
Klein, F.      5 315 377 444
Knopp, M.I.      42 44 327 330
Koblitz, N.I.      29
Koehler, G.      6
Kondo, T.      6 72 366
Koornwinder, T.H      13
Kumbakonam      2
Lamphere, R.      10 29 79
Landen's transformation      113 126 146Ч147 213
Landen, J.      5 146 181
Langebartel, R.      169
Lattice gases      6
Legendre functions      89
Legendre Ч Jacobi symbol      329
Legendre's relation      455Ч456
Legendre, A.M.      5 107 181 220 232 234 244
Lepowsky, J.      78
Lie algebras      78
Ling, C.-B.      140 142
Littlewood, D.E.      311
Littlewood, J.E.      2
Macdonald identities      32
Macdonald, I.      32
Maclaurin, C.      146
MacMahon, P.A.      113
Macsuma      10 312 369 372 377 400 408 416Ч417 425 430 488
Mathematica      10
Medial section      298
Mehler Ч Dirichlet integral      89
Mermin, N.D.      151
Metius, A.      194
Milne, S.      32
Mimachi, K.      32
Mittag Ч Leffler theorem      144
Mixed modular equation, defintion      325
Mixed modular equations, table of degrees      325Ч326
Moak, D.S.      29
Modular equation, definition      213
Modular equations      3Ч8
Modular equations of degree 11      363Ч372
Modular equations of degree 119      430Ч435
Modular equations of degree 13      376Ч377
Modular equations of degree 135      430Ч435 449Ч453
Modular equations of degree 143      430Ч435
Modular equations of degree 15      383Ч397 435Ч439
Modular equations of degree 16      216
Modular equations of degree 17      397Ч400
Modular equations of degree 175      449Ч453
Modular equations of degree 19      416Ч417
Modular equations of degree 2      214
Modular equations of degree 207      449Ч453
Modular equations of degree 21      400Ч408
Modular equations of degree 23      411Ч416
Modular equations of degree 231      449Ч453
Modular equations of degree 247      449Ч453
Modular equations of degree 25      290Ч297
Modular equations of degree 255      449Ч453
Modular equations of degree 27      360Ч362
Modular equations of degree 3      230Ч238 352Ч353
Modular equations of degree 31      439Ч444
Modular equations of degree 33      408Ч411
Modular equations of degree 35      423Ч426 430
Modular equations of degree 39      426Ч430 435Ч439
Modular equations of degree 4      214Ч215
Modular equations of degree 47      444Ч449
Modular equations of degree 5      280Ч288
Modular equations of degree 55      426Ч430 435Ч439
Modular equations of degree 63      426Ч435 435Ч439
Modular equations of degree 7      314Ч324 435Ч437
Modular equations of degree 71      444Ч449
Modular equations of degree 8      216Ч217
Modular equations of degree 87      449Ч453
Modular equations of degree 9      352Ч358
Modular equations of degree 95      430Ч435
Modular equations, table      8 325Ч326
Modular form, definition      328
Modular forms      7 326Ч345 366Ч376 399Ч408 415Ч417 423Ч425 430 484Ч488
Modular group      327
Modulus      4Ч5 102
Molk, J.      6 45 72
Mordell, L.J.      2 83 261
Moreau, C.      200
Mueller, R.      10
Muir, T.      147 150
Multiplier      5 214 230
Multiplier system      7 328Ч329
Multiplier system of Dedekind eta-function      330
Multiplier systems for theta-functions      330Ч332
National Science Foundation      10
Notation      10 12 88Ч89 230Ч231 326Ч329
Nyvoll, M.      147
Odlyzko, A.M.      79
Order of a modular form      328
Orders of theta-functions at rational cusps      333
Partial fraction expansions      200Ч206
Partition function      262
Paule, P.      78
Peano, G.      147 150
Pendulum      212Ч213 243Ч244 246 299Ч301
Perfect series      42
Perron, O.      166Ч167 186 208
Peterson, D.H.      398
Petersson, H.      326
Pfaff's transformation      17
Pi, approximations to      151Ч152 194Ч196
Playfair, J.      146
Preece, C.T.      163Ч164
Privman, V.      80
Proceedings of the London mathematical society      77
Psi function      88
Pure series      42
Purtilo, J.M.      7 10 326
q-analogue of Dougall's theorem      15
q-analogue of Gauss' theorem      14
q-beta integral      11
q-binomial theorem      14 32
q-gamma function      13
q-series      11Ч12 14Ч19 21Ч34
Quintic algorithm for calculating pi      269
Quintuple product identity      11 32 56Ч57 59 80Ч83 338
Rademacher, H.      218 273 330
Raghavan, S.      7 113 262Ч263 324
Rahman, M.      29
Rama Murthy, C.      10
Ramamani, V.      18 31 54
Ramanathan, K.G.      4 7 10 20 28 79 82 84 86 221Ч222 262 265 274 276 324 347
Ramanujan Centenary prize competition      246
Ramanujan's $_1\psi_1$ summation      11 31Ч34
Ramanujan's quarterly reports      29
Ramanujan's theta-function      18
Rangachari, S.S.      7 113 263 324
Rankin, R.A.      326 328Ч329 332Ч333 342 370 373 484
Rao, K.S.      79
Rao, M.B.      140
Reciprocal of a modular equation      216
Reciprocal relation      334
Riesel, H.      140
Rogers Ч Ramanujan continued fraction      11 30Ч31 79Ч80 267
Rogers Ч Ramanujan continued fraction, combinatorial interpretation      79Ч80
Rogers Ч Ramanujan continued fraction, finite form      31
Rogers Ч Ramanujan identities      11 77Ч79
Rogers, L.J.      14 18 30 77Ч79 144 163 166Ч168 207 398
Rothe, H.A.      14
Row-column method of summation      114
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