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Электронная библиотека Попечительского совета
механико-математического факультета
Московского государственного университета
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| Bruce C.Berndt - Ramanujan's Notebooks (part 3) |
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| Предметный указатель |
 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. 10 147 149-150 456
Andrews, G.E. 10 13-15 18 28-29 32 36-37 77-80 83 347 398
Askey, R. 2 10 14 29 32 77-79 149
Atkin, A.O.L. 83
Ayyar, M.V. 140
Bailey, D.H. 6
Bailey, W.N. 15-17 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 79 111-112 140-141 147 150 172 197 326 456
Bernoulli numbers 42 61-64 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 154-155
Cauchy, A. 14 140
Cayley, A. 2-3 5 106-107 135 138 218 220 232 241
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 19-29 92 146 151 163-168 185-187 206-208 221-222 345-347
Cosine identity 345 347-348
Court, N.A. 245
Coxeter, H.S.M. 245
Cusp 328
Cusp parameter 328
Darling, H.A. 261
Dedekind eta-function 37 44 330-338
Degree of a modular equation 4
Degree of a modulus 229
Degree of series 42
Denis, R.Y. 28 78-79
Deutsch, J. 6
Dickson, L.E. 197 200
Digby, K. 200
Dimidiation 126 178
Diophantine equations 197-200
Divisor functions 62 64-65
Duplication 125 127-128 178
Dyson, F.J. 10 83
Eccentricity of an ellipse 145
Ehrenpreis, L. 78
Eisenstein series 7 65 121-122 126-139 144-145 175-177 454-488
Eisenstein series, values in terms of elliptic function parameters 126-129
Eisenstein, G. 28
Ellipse, approximations to the perimeter of 145-150 180-189
Elliptic curve 6
Elliptic functions 2-3
Elliptic functions, notation 101-102
Elliptic integral of the first kind 4 102
Elliptic integral of the second kind 176-177 303-304
Elliptic integrals 104-113 238-243 297-298
Elliptic integrals, addition theorem for elliptic integrals of the first kind 106-108
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 197-199
Euler's partition theorem 37
Euler's pentagonal number theorem 36-37
Euler, L. 14 37 147 150 196-197 199
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 190-196 211-213 243-249 298-302
Gerst, I. 73 83
Ghosh, S. 488
Glaisher, J.W.L. 169 242 303
Glasser, M.L. 80 110 113
Gordon, B. 78-79 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 29-32 36 39 45 77 79 84 86 126 162-164 197 199 262 326 346 385 426 450
Hecke operator 373
Hecke, E. 398
Heine's continued fraction 21
Heine, E. 11 14-15 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 140-141 157-162
Hyperbolic function series evaluations in terms of elliptic function parameters 132-139 153-157 172-178
Hyperbolic function series identity 162
Hypergeometric differential equation 120-121
Hypergeometric functions 3 5 88-104 120-122 144-150 153-155 185-186 213 238-239 289-290 455-456
Invariant order of a modular form 328
Inversion formula for base q 100
Ismail, M.E.H. 32 42 79
Ivory, J. 146-147
Jackson, F.H. 14-15
Jackson, M. 32
Jacobi triple product identity 11-12 32 35-36
Jacobi's identity 39
Jacobi's imaginary transformation 106 154
Jacobi, C.G.J. 3 5 11 14 36 39 54 87 115-116 123 126 135 143 165-166 169 173 176-177 207 218 220 232 234 239-241
Jacobian elliptic functions 3 54 87 107-108 135-136 138-139 143 162-163 165-180 207-208 227 242 304
Jacobian elliptic functions, conversions of old formulas into new formulas 173-174
Jacobsen, L. 10 20 22-24 26-27 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 113 126 146-147 213
Landen, J. 5 146 181
Langebartel, R. 169
Lattice gases 6
Legendre functions 89
Legendre - Jacobi symbol 329
Legendre's relation 455-456
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 10 312 369 372 377 400 408 416-417 425 430 488
Mathematica 10
Medial section 298
Mehler - Dirichlet integral 89
Mermin, N.D. 151
Metius, A. 194
Milne, S. 32
Mimachi, K. 32
Mittag - Leffler theorem 144
Mixed modular equation, defintion 325
Mixed modular equations, table of degrees 325-326
Moak, D.S. 29
Modular equation, definition 213
Modular equations 3-8
Modular equations of degree 11 363-372
Modular equations of degree 119 430-435
Modular equations of degree 13 376-377
Modular equations of degree 135 430-435 449-453
Modular equations of degree 143 430-435
Modular equations of degree 15 383-397 435-439
Modular equations of degree 16 216
Modular equations of degree 17 397-400
Modular equations of degree 175 449-453
Modular equations of degree 19 416-417
Modular equations of degree 2 214
Modular equations of degree 207 449-453
Modular equations of degree 21 400-408
Modular equations of degree 23 411-416
Modular equations of degree 231 449-453
Modular equations of degree 247 449-453
Modular equations of degree 25 290-297
Modular equations of degree 255 449-453
Modular equations of degree 27 360-362
Modular equations of degree 3 230-238 352-353
Modular equations of degree 31 439-444
Modular equations of degree 33 408-411
Modular equations of degree 35 423-426 430
Modular equations of degree 39 426-430 435-439
Modular equations of degree 4 214-215
Modular equations of degree 47 444-449
Modular equations of degree 5 280-288
Modular equations of degree 55 426-430 435-439
Modular equations of degree 63 426-435 435-439
Modular equations of degree 7 314-324 435-437
Modular equations of degree 71 444-449
Modular equations of degree 8 216-217
Modular equations of degree 87 449-453
Modular equations of degree 9 352-358
Modular equations of degree 95 430-435
Modular equations, table 8 325-326
Modular form, definition 328
Modular forms 7 326-345 366-376 399-408 415-417 423-425 430 484-488
Modular group 327
Modulus 4-5 102
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 7 328-329
Multiplier system of Dedekind eta-function 330
Multiplier systems for theta-functions 330-332
National Science Foundation 10
Notation 10 12 88-89 230-231 326-329
Nyvoll, M. 147
Odlyzko, A.M. 79
Order of a modular form 328
Orders of theta-functions at rational cusps 333
Partial fraction expansions 200-206
Partition function 262
Paule, P. 78
Peano, G. 147 150
Pendulum 212-213 243-244 246 299-301
Perfect series 42
Perron, O. 166-167 186 208
Peterson, D.H. 398
Petersson, H. 326
Pfaff's transformation 17
Pi, approximations to 151-152 194-196
Playfair, J. 146
Preece, C.T. 163-164
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 11-12 14-19 21-34
Quintic algorithm for calculating pi 269
Quintuple product identity 11 32 56-57 59 80-83 338
Rademacher, H. 218 273 330
Raghavan, S. 7 113 262-263 324
Rahman, M. 29
Rama Murthy, C. 10
Ramamani, V. 18 31 54
Ramanathan, K.G. 4 7 10 20 28 79 82 84 86 221-222 262 265 274 276 324 347
Ramanujan Centenary prize competition 246
Ramanujan's  summation 11 31-34
Ramanujan's quarterly reports 29
Ramanujan's theta-function 18
Rangachari, S.S. 7 113 263 324
Rankin, R.A. 326 328-329 332-333 342 370 373 484
Rao, K.S. 79
Rao, M.B. 140
Reciprocal of a modular equation 216
Reciprocal relation 334
Riesel, H. 140
Rogers - Ramanujan continued fraction 11 30-31 79-80 267
Rogers - Ramanujan continued fraction, combinatorial interpretation 79-80
Rogers - Ramanujan continued fraction, finite form 31
Rogers - Ramanujan identities 11 77-79
Rogers, L.J. 14 18 30 77-79 144 163 166-168 207 398
Rothe, H.A. 14
Row-column method of summation 114
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