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| Jones W.B., Thron W.J. — Continued fractions: Analytic theory and applications |
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| Предметный указатель |
Mandell, M. 63 413
Markoff theorem 256 344
Markoff, A. 343 413
Maurer, G.V. 198 258 413
McCabe, J. 15 130 197 198 257 258 261 266 267 413
McGregor, J.L. 365 412
Mechanical quadrature 6 7
Merkes, E.P. 385 410 46 298 307 413
Meromorphic function 131
Metric theory of continued fractions 4
Miller, S.C 198 413
Minimal solution 163 397
Minimal solution, Numerical instability 167—169 397
Modified regular C-fraction 333—334 387
Modified S-fraction 334 387
Moment problems, Hamburger 331
Moment problems, Stieltjes 331
Moment problems, Strong Stieltjes 332
Moment theory 8 9
Moment theory, Solutions of moment problems 342—343
Montroll, E.W. 197 410
Multiple parabola theorem 106
Murphy, J.A. 258 406 15 130 197 198 257 266 267 413 198 221 261 365 414
Necessary conditions for convergence 78
Newton — Pade approximants 195—196 394
Noerlund, Niels E. xxv 196 414
Norm 21
Normal fps 189
Normal Pade approximant 188
Normed field 21
nth denominator 20
nth numerator 20
O'Donohoe, M.R. 15 198 221 365 376 414
Odd part 42
Order of correspondence 149
Orthogonal polynomials 6 7 250—255
P-fraction 159 390
P-fraction, Correspondence 159—160
P-fraction, Relation to Pade table 193 390
Pade approximant 187
Pade table 7 187
Pade, H. 7 185 414
Para-odd 285
Parabola theorem 105
Parabolic convergence regions 13
Parabolic element regions 75
Parabolic l.f.t. 49
Paraconjugate 283
Partial denominator 17
Partial numerator 17
Paydon, J.F. 13 99 134 414
Periodic continued fraction 46
Perron, O. 221 408 xxiii xxv 7 22 23 46 90 93 107 108 125 126 148 172 185 194 198 251 254 256 257 276 331 335 340 342 343 385 390 392 414
Pfluger, Pia xxiv 313 320 350 410
Phipps, Thomas E., Jr. 198 414
Pincherle theorem (generalized) 164 403
Pincherle, S. 10 15 148 163 164 414
Piranian, G. 63 407
Plasma dispersion function 219
Poincare, H. 8 414
Polya frequence (PI7) series 237
Positive definite J-fraction 129 389
Positive definite J-fraction, Convergence 138
Positive definite J-fraction, Truncation error bounds 325—326
Positive rational function 284
Positive T-fraction 130 391
Positive T-fraction, Convergence 146
Positive T-fraction, Truncation error bounds 316—317
Preece, C.T. 7 414
Pringsheim convergence criterion 92
Pringsheim, A. 10 11 13 19 46 60 92 98 126 181 415
Queuing problem 374
Quotient-difference (QD) algorithm 228—235
Quotient-difference table (qd-table) 227—228
Ramanujan, S. 7 415
Rational expression 185
Real J-fraction 130 389
Real J-fraction, Truncation error bounds 326—327
Region 64
Regular C-fractions 7 129 386
Regular C-fractions, Connection with qd-algorithm 228—233
Regular C-fractions, Convergence 131—132 182—183
Regular C-fractions, Correspondence 222—227
Regular C-fractions, Relation to Pade table 190—191 387—388
Regular continued-fraction expansion 2 22
Reid, Walter M. 73 298 415
Repulsive fixed point 52
Ritt, J.F. 330 415
RITZ fraction 387
Roach, F.A. xxv 83 84 307 415
| Rouche, E. 8 415
Rutishauser, H. xxiv 15 221 227 235 267 415
S-fraction 129 386
S-fraction, Convergence 136
S-fraction, Equivalent forms 315
S-fraction, Numerical stability of BR algorithm 358—363
S-fraction, Truncation error bounds 312—314
Sack, R.A. 249 415
Salt, E.B. xxiv 185 196 415
Schlomilch, O. 6 198 415
Schoenberg, I.J. 222 237 415
Schoenberg, Karlin Theorem 237
Schur continued fraction 392
Schur, I. 392 415
Schwenter, D. 2 3 416
Schwerdtfeger, H. 46 416
Scott, W.T. 46 156 385 413 13 90 98 382 416 113 125 418
Seidel — Stern theorem 87
Seidel, L. 10 87 416
Sequence of convergence regions 78
Shanks, D. 185 416
Sheng, P. 197 416
Shohat, J. 9 333 343 416
Simple convergence region 78
Simple sequence 308
Singh, D. 115 383 4/6
Singular points, location of 381—385
SITZ fraction 387
Slavik, Josef 258 408
Snell, R. 62 94 105 126 298 305 322 411
Sobhy, M.I. 198 416
Stable (or Hurwitz) polynomial 283
Stable (or Hurwitz) polynomial, Necessary and sufficient conditions 290 293 295—296
Stegun, Irene A. 168 216 218 347 400 404 198 416
Stera — Stolz theorem 79
Stern, M.A. 7 10 78 79 87 416
Stieltjes fraction 386
Stieltjes — Vitali theorem 89 130—131
Stieltjes, T 7 8 9 15 63 89 131 135 136 250 331 416
Stoer, J. 196 416
Stolz, O. 46 78 79 416
Sweezy, W.B. 298 302 416
Szasz, O. 10 126 417
Szegoe, G. 254 255 256 343 417
T-fraction 130 256 390
T-fraction, Correspondence to rational functions 380—381
T-fraction, Expansions for families of bounded functions 377—380
Tamarkin, J.D. 333 343 416
Tannery, Jules 198 417
Tchebycheff, P. 8 9 15 248 250 417
Thacher, Henry C, Jr. 196 198 417
Thale, James S. 385 417
Thiele continued fraction 196 393
Thiele continued fraction, Connection with Newton — Pade table 394
Thiele, T.N. 46 196 417
Thome, L.W. 7 10 417
Thron, W.J. 383 384 405 63 124 406 94 410 xxiv 13 14 15 60 62 68 69 71 80 94 98 99 106 107 115 124 125 147 181 185 197 256 257 261 298 308 310 312 325 331 342 351 353 358 382 411 115 124 412 76 99 115 134 413 115 298 302 383 416 13 69 75 89 91 99 101 105 106 107 108 115 124 125 137 181 298 305 322 382 383 417 13 63 94 99 106 125 197 221 257 261 298 329 418
Totally positive sequence 236
Truncation error of nth approximant 297
Truncation error of nth approximant, a posteriori bounds 306
Truncation error of nth approximant, a priori bounds 306
Tukey, J. 196 417
Twin convergence regions 13 78 115 124 125
Two-point Pade approximant 195—196 391—392
Unifonn convergence of a sequence of meromorphic functions 176
Unifonn sequence of convergence regions 99
Unifonn simple convergence region 99
Uniform parabola theorem 76 99
Uniform twin convergence region 99
Uniformly bounded sequence 176
Univalent functions 385
Value region 64
Van Vleck theorem 88
Van Vleck, E.B. 9 10 13 60 88 89 90 115 132 140 145 418
Varga, R.S. xxiv 185 415
Waadeland, H. 15 331 342 411 16 256 298 329 331 377 378 379 381 418
Wall, H.S. 115 406 126 412 13 125 413 13 99 134 414 13 90 98 382 416 xxiii—xxv 13 15 63 89 90 99 106 113 115 125 126 127 128 138 185 198 250 283 295 331 347 382 241 248 388 389 418
Wallin, H. 197 412
Wallis, J. 2 3 5 419
Warner, D.D. 196 419
Watkins, Bruce O. 235 410
Watson, G.N. 7 167 419
Wetzel, M. 13 106 115 419
Wheeler, J.C 249 419
Widder, D.V. 198 333 419
Worpitzky theorem 94
Worpitzky, J. 10 13 60 75 94 98 183 419
Wuytack, L. xxiv xxv 15 185 196 419
Wynn, P. xxiv xxv 185 198 258 276 298 328 329 419
Zucker, Ruth 198 416
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