Авторизация
Поиск по указателям
Wong R. — Asymptotic approximations of integrals
Обсудите книгу на научном форуме Нашли опечатку?
Название: Asymptotic approximations of integralsАвтор: Wong R. Аннотация: Asymptotic methods are frequently used in many branches of both pure and applied mathematics, and this classic text remains the most up-to-date book dealing with one important aspect of this area, namely, asymptotic approximations of integrals. In Asymptotic Approximations of Integrals , all results are proved rigorously, and many of the approximation formulas are accompanied by error bounds. A thorough discussion on multidimensional integrals is given, and references are provided. Asymptotic Approximations of Integrals contains the "distributional method," which is not available elsewhere. Most of the examples in this text come from concrete applications.
Since its publication twelve years ago, significant developments have occurred in the general theory of asymptotic expansions, including smoothing of the Stokes phenomenon, uniform exponentially improved asymptotic expansions, and hyperasymptotics. These new concepts belong to the area now known as "exponential asymptotics." Expositions of these new theories are available in papers published in various journals, but not yet in book form.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2001Количество страниц: 543Добавлена в каталог: 05.12.2013Операции: Положить на полку |
Скопировать ссылку для форума | Скопировать ID
Предметный указатель
Locally absolutely continuous function 250 Logarithmic integral 43 Logarithmic integral, asymptotic expansion of 43 Logarithmic singularity 66 144 145 185 Lorch, L. 208 Lord Kelvin 76 Love, E.R. 352 Luke, Y.L. 153 Maclaurin coefficients, asymptotic behavior of 116—127 145 Mahony, J.J. 352 Malgrange, B. 291 454 Marichev, O.I. 192 Markushevich, A.I. 397 Maslov, V.P. 515 McClure, J.P. 73 177 290 291 323 344 351 352 466 476 485 Meinardus, G. 291 Mellin transform technique 147 351 Mellin transforms 147 Mellin transforms, (relation with) bilateral Laplace transform 149 Mellin transforms, analytic continuation 153 Mellin transforms, convolution integral 147 151 333 352 Mellin transforms, generalized 337 Mellin transforms, inversion formula 147 151 Mellin transforms, Parseval formula (or Parseval identity) 148 189 Mellin transforms, properties of 149 Mellin transforms, table of 192—194 Mellin — Barnes type integrals 228 Method of steepest descents 84 144 145 Meyer, R.E. 355 Miller, J.C.P. 388 Minetti, B. 210 240 Morse's lemma 479 Morse, M. 479 Moser, L. 142 143 145 Multiple integrals 177 477 Multiple Integrals, resolution of 280 Murray, J.D. 54 Nesting property 281 Neutralizers 246 Noble, B. 480 510 Oberhettinger, F. 154 156 170 171 192 324 422 Olver, F.W.J. 4 9 13 24 30 38 54 66 77 81 83 143—146 196 200 211 220 240 352 355 364 383 388 403 406 421 422 Open covering 246 Orszag, S.A. 82 Osborn, T.A. 230 240 Oscillatory kernels 216 Ott, H. 421 Otter, R. 142 Parabolic cylinder function 236 364 Parseval formula see "Mellin transform" "Fourier Partition of unity 246 Pearcey integral 388 395 Pearcey integral, uniform asymptotic expansion of 416 417 Pearcey, T. 388 Pederson, R.N. 143 Perron's method 103 145 405 Perron, O. 103 145 Peters, A.S. 146 Phase function 76 phase velocity 83 Phragmen — Lindeloef theorem 165 Plemelj formula 313 Plemelj, J. 313 Pochhammer notation 47 Poincare, H. 4 10 Positive definite functions 281 Poston, T. 479 491 512 Pourahmadi, M. 408 Principle of Stationary Phase 76 144 240 Quadrature formulae for Bessel transforms 226 Quadrature formulae for Fourier transforms 222 Quadrature formulae, Gauss — Laguerre 222 Quartic transformation 392 Rabinowitz, P. 222 Rapidly decreasing functions 261 266 Ray, B.K. 73 Recessive (exponentially decreasing) 94 Regularization 257 Regularization at infinity 260 261 Regularization in finite interval 259 Regularization of a function 268 Regularization of an integral 258 336 Regularization, method of 333 362 Regularization, nonuniqueness 272 Resolution of singularities see "Singularities" Riekstins, E. 13 64 144 Riemann — Lebesgue lemma, generalized 200 Riemann — Liouville fractional integral see "Fractional integral" Riemann, B. 76 Robinson's conjecture 120 Robinson, R. 120 Rosov, V.A. 452 Rosser, J.B. 54 Rudin, W. 2 51 78 151 207 248 262 254 262 290 291 327 509 Ryzhik, I.M. 169 434 437 439 Saddle point 85 432 Saddle point of order m 87 Saddle point, many coalescing 383 Saddle point, near a pole 356 Saddle point, near an endpoint 360 Saddle point, relevant 89 Saddle point, two coalescing 366 Saddle-point method 103 Sather, J.O. 515 Schlaefli's integral 97 Schmidt, H. 10 Schoenfeld, L. 142 146 Schroedinger spectral kernel 230 Schwartz, L. 278 290 502 Scorer's function 419 Second fundamental form of differential geometry 511 Servadio, S. 218 476 Shaffer, D.H. 515 Shao, T.S. 224 Shilov, G.E. 241 248 273 290 291 Shivakumar, P.N. 54 409 515 Signature of a matrix 480 Sine integral 513 Singularities, resolution of 492 Sirovich, L. 54 Smith, K.T. 489 Soni, K. 19 54 176 191 192 240 422 Soni, R.P. 191 240 Splitting lemma 491 512 Stationary phase see "Principle of stationary phase" Stationary phase approximation 77 240 Stationary phase approximation for double integrals 431 Stationary phase approximation, n-dimensional analogue 478 Stationary points 77 424 478 Stationary points, boundary 440 484 Stationary points, curve of 452 Stationary points, degenerate 435 491 Stationary points, non-degenerate 487 Steepest ascent 87 Steepest descent 86 87 see Steffensen, J.F. 38 Stegun, I.B. 82 222 Stenger, F. 225 Stewart, I. 479 491 512 Stiltjes transform 147 295 304 351 Stiltjes transform, asymptotic expansion of 299 300 303 307 308 Stiltjes transform, error bounds for 302—304 309 Stiltjes transform, generalized 185 Stiltjes transform, generalized, asymptotic expansion of 186 Stirling formula 1 51 62 Stirling numbers 143 Stirling numbers, asymptotic expansion of 143 Stirling series 51 Stokes line 94 Stokes' phenomenon 94 Stokes, G.G. 76 94 Stoyanov, B.J. 192 Struik, D.J. 511 Summability method 195 216 Support of a distribution 245 Support of a function 242 Surface distribution 241 280 Swallowtail integral 388 389 Swallowtail integral, uniform asymptotic expansion of 395 Szegoe, G. 41 54 119 143 207 225 396 420 422 Tangential contact, points of 487 Tauberian theorem see "Laplace transforms" Taylor series for 273 Taylor series for 270 Taylor series for the 288 Telegrapher's equation 131 Temme, N.M. 366 421 422 Tempered distributions 261 262 Tempered distributions in 267 Tempered distributions, Fourier transform of 276 Test function space 243 Test functions 242 243 Thorpe, J.A. 511 Titchmarsh, E.C. 165 191 192 195 197 375 398 Tolstov, G.P. 41 Transformations, cubic 367 Transformations, quartic 392 Transformations, rational 396 transforms see "Bessel transform" "Fourier "Hankel "Hilbert "Kontorovich "Laplace "Mellin Translation of a distribution 249 286 Translation of a function 286 Tricomi, F.G. 54 66 Uniform asymptotic expansion 356 Uniform asymptotic expansion of complementary incomplete Gamma function 365—366 Uniform asymptotic expansion of Laguerre polynomials 381 402 Uniform asymptotic expansion of Legendre fUnction of the first kind 408 Uniform asymptotic expansion of Legendre polynomial 420 Uniform asymptotic expansion of Pearcey integral 416—417 Uniform asymptotic expansion of swallowtail integral 395 Ursell, F. 146 192 319 321 367 368 387 392 397 421 422 Uspensky, J.V. 391 Valleys 87 van der Corput, J.G. 77 246 421 Van der Waerden, B.L. 360 Van Kampen, N.G. 423 von Stacho, T. 230 Watson's lemma 20 Watson's Lemma for loop integrals 54 355 Watson's lemma, converse 31 Watson's lemma, generalized 22—24 Watson, E.J. 31 Watson, G.N. 3 20 41 76 77 144 192 407 413 417 Weber parabolic cylinder function 236 Weber parabolic cylinder function, integral representation of 236 Weber's function 82 Weights 222 Weiss, G. 222 Whittaker function 410 421 Whittaker, E.T. 185 Widder, D.V. 22 30 143 149 150 151 223 Wimp, J. 54 WKB approximation 4 Wolf, E. 475 Wong, R. 54 73 129 144 145 146 172 177 191 192 215 230 240 290 291 317 323 326 344 361 352 409 421 422 466 476 485 515 Wright, E.M. 144 Wyman, M. 13 22 54 103 121 142—146 Yap, W.T. 153 Zauderer, E. 144 146 Zayed, A.I. 351
Реклама
-function 
|
|
О проекте