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Dingle R. Ч Asymptotic Expansions: Their Derivation and Interpretation
Dingle R. Ч Asymptotic Expansions: Their Derivation and Interpretation

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Ќазвание: Asymptotic Expansions: Their Derivation and Interpretation

јвтор: Dingle R.

язык: en

–убрика: ћатематика/јнализ/јсимптотические методы, “еори€ возмущений/

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

ed2k: ed2k stats

√од издани€: 1973

 оличество страниц: 521

ƒобавлена в каталог: 26.03.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Abel      v x 26 53
Absolutely convergent series      14 75Ч80
Accelerating convergent series      403
Accuracy obtainable from terminant expansions      300 459Ч461 466Ч467 492Ч493
Additional stationary point      455 457 459 481
Additivity of contributions from expansion points      ix 131Ч133 141Ч142 458
Aerodynamics      277
Airey      vi viii x 54 217 254 403Ч404 408 429
Airy functions      22Ч23 51 240Ч241 279 291Ч292
Alternating asymptotic series      v vi 401Ч402
Anger function      80 108 202Ч203 230 250 376Ч378 380 386Ч389 396 398Ч399 450 485 511Ч512
Applied mathematics      14 277
Associated function      6 148Ч149
Associated Legendre polynomial      71 72
Astronomy      277
Asymmetrical saddle points      467
Asymptotic power series      2 26Ч55 100Ч109 275Ч284 371Ч381 431Ч451
Asymptotics      v
Bailey, V. A.      328 330
Bailey, W. N.      55
Baker      403 429
Barnes      55 139 183 208 309 320 381
Basic terminants      198 406 415Ч429 484
Beer      55
Berghuis      215
Bernoulli numbers      75 91 92
Bernoulli polynomials      46 47 336
Berry      14 24
Bessel functions      36 50 51 54 62Ч65 78 82 86 95Ч97 101 104Ч105 108 166Ч174 200Ч202 240Ч241 248 250Ч251 281Ч282 283 286 303Ч307 334Ч339 349 440Ч441 449Ч451 467Ч472 482Ч485 495
Bessel functions of nearly equal order and argument      170Ч172 174 250Ч251 339 470Ч472 482Ч484
Bessel functions of the third kind      50 62 64 65 78 96 101 104Ч105 108 181Ч182 189 201 212 277 349 440Ч441 485
BesselТs addition theorems      200
Bickley      468 488
Bijl      139
Binet      66 98 99 105 436
Binomial expansion      4 40 44 47
Blanch      54 130
Bleistein      215 254
Blumenthal      317 320
Borel summation      405Ч408 429
Bose Ч Einstein condensation      267Ч271
Bose Ч Einstein integral      53 69 73 98Ч99 109 449
Boundary layers      14
Bounds to remainders      ix 401Ч403 405 488
Bowen      54 198 208
Braun      215
Bremmer      215
Brillouin      317 320
Buchholtz      54
Budden      320
Burmann series      405
Busbridge      54
Carleman      430
Carlini      316 320
Cauchy      v 26 53 128 130 132 133 139
Chako      215
Chase      55
Chemistry      277
Cherry      349 403 430
Chester      247 254
Choquard      55
Circulis      139
Classification of series      v 13Ч15 68Ч80 277
Code      408 410
Complete asymptotic expansions      vi 8 19
Complete elliptic integrals      71
Conditionally convergent series      14 68Ч75
Confluent hypergeometric functions      24 33Ч35 46 50 60Ч62 94Ч95 103Ч104 175Ч180 203 249 275Ч277 279Ч281 286 356Ч362 366Ч369 370 438Ч440 486 504Ч505
Connection formulae      288Ч295 298 301 303 355Ч366 386 491Ч492 497 503 510Ч511
Continuation formulae, basic terminants      418
Continuation formulae, confluent hypergeometric function      33
Continuation formulae, error function      6 12
Continuation formulae, factorial      38
Continuation formulae, modified Bessel function      36
Continuation rules for asymptotic expansions      6Ч8 413Ч415
Continued fractions      403
Controversies about connection formulae      292Ч295
Convention adopted on fractional powers      12Ч13
Conventions adopted on cube roots of -1 and $\pm i$      147
Convergent power series listed      68Ч80
Convergent Series      1 26 53 403
Converging factor      ix
Conversion by power identification      116 122 127 248Ч249 253
Conversion of power series into integral representations      56Ч99
Conwell      107 109
Copson      x xi
Correspondences between late and early terms      148 151 300 303
Correspondences between quadratic and cubic contours      137 171 174 187 194 232
Cosine integral      77 447
Courant      140 154
Critical points      131
Crothers      295 320
Cube root conventions      147
Cube roots      123 136
Cubic contours      136Ч137
Cut in complex plane      13
Darboux method for calculating late terms in power series      4 24 140Ч142 152Ч154 157 409 411
Darwin      330
Darwin Ч Fowler method of selector variables      268
Davis      54 140 154
DawsonТs integral      224 263Ч264 273 274
de Haas-van Alphen effect      14
De Morgan      26 53
Debye      133 139
Defining asymptotic expansions      v viii 16Ч21
defining functions      26Ч27 277
Derivatives, high      155Ч157
Difference equations      viii 339
Difference expansions      433 451
Dingle      vi vii xi 6 19 20 24 54 55 107 109 130 268 274 295 317 320 380 381 395 404 405 419 430 4A1 451 463 488
Dirichlet      26 53
Discontinuities in basic terminants      411Ч412 428 501
Dispersion relations      480 482 484
Distributions over geometrical progressions and basic terminants      408 415 431
Dixon      43 55
Doetsch      53 54
Double integrals      209Ч215
Dougall      277 284
Duhamel      53
Dunham      330
Duplication formula for factorials      42
DТAlembert      26 53
Earthquakes      14 318
eigenvalue problems      vii 17 325 362 411 495
Elliptic integrals      71
Engineering      277
Erdelyi      x xi 24 54 55 248 320 321 349
Error function      1Ч2 5Ч6 12Ч13 18 20 26Ч27 29 30 76 282 403Ч404 413
Euler      v xi
Euler constant      30 37 66 73 83
Euler numbers      75 92
Euler polynomials      46
Euler transformation      15
Evgrafov      321
Expansion points, alternative      107 271Ч272
Exponential base      129
Exponential integral      31Ч33 54 59Ч60 76 94 102 103 162 434Ч435
Exponential type of series      14
Extinction point      ix 354 500
Factorial function      10 37Ч38 65Ч66 105Ч106 157Ч160 435Ч436 448 461Ч462
Factorial function, incomplete      30Ч31 44 57Ч59 77 93 102 160Ч164 249 283 361 369Ч370 415 434Ч435 462Ч464 480Ч481 506
Factorial sequences      431Ч434
Fedorcuk      321
Fermi Ч Thomas calculations      14
Fermi-Dirac integral      20 38Ч39 55 66Ч67 69 74 106 164Ч166 436Ч437.
ferromagnetism      14
Flamme      140 154
Focke      215
Ford      49 55
Fractional powers      12Ч13
Franklin      107 109
Fraser      268 274
Fresnel integrals      77 446 451
Friedman      107 709 247 254
Frobenius      26 53 275 284
Froman, N. and P. O.      294 295 317 321
Furry      321 330
GANs      292 316 321
Gegenbauer polynomials      45 47
General exponential integral      102 162
Geometrical progression      406
Goldstein      17 25 317 321
Goodwin      403 430 446 451
gray      54
Green      v xi 285 287 288 292 294 316 321 323
Gregory      26 53 433 451
Gunson      vii xi
Haar      140 154
Hamy      140 154
Handelsman      54 215
hankel      39 277 284
Heading      6 25 295 321
Hermite polynomials      46 47
High derivatives      155Ч157
hilbert      140 154
Historical remarks      v-vii 13Ч14 16 26 107 132Ч134 140 216Ч218 241 247Ч248 275Ч278 292Ч295 316Ч318 327Ч329 401Ч405 408
Hobson      64 99
homogeneous differential equations      275Ч370 489Ч506
Horn      276 284
Hsu      215
Hydrodynamics      14 277
Hypergeomctric function      14 15 72 88
Ikaunieks      451
Incomplete factorial function      30Ч31 44 57Ч59 77 93 102 160Ч164 249 283 361 369Ч370 415 434Ч435 462Ч464 480Ч481 506
Incomplete gamma function      54
Indentations in contour      30 280
inhomogeneous differential equations      371Ч400 507Ч513
Integrals of Bessel functions      450Ч451
Integration by parts      21 112 404
Integration constants in recurrence relations      297 300 303 333 355Ч356 386
Interchanging order of summation and integration      410
Interdependence of late and early terms in asymptotic expansions      148Ч149 151 152 299Ч300 303
Interpretation of asymptotic expansions      vi 401Ч513
Inverse factorial sequence      431Ч432
Ionosphere      14 318
Ising model      14 15
Ittman      321
Jacobi polynomials      45
Jacobian      211
Jeffreys      x xi 292 295 317 321 404 430
Jones      215
JORDAN      156 199 208
Jorna      x xi 317 318 321 346 350 362 473 488
Kato      vii xi
Kazarinoff      350 362
Kelvin      134 139
Kelvin functions      78
Kemble      317 321
Kline      215
Kontorovitch      215
Kramers      292 317 321
Kreyszig      447 451
Kummer relation      33 50 54 61 175 357 447 451
Lagrange reversion theorem      112 127Ч130
Laguerre function      46 163 283
Landsberg      268 274
Lang      224 254
Laplace      v xi 130 133 139
Laplace-type representations      27 100 276 409 410
LaplaceТs method for expanding integrals      133
Late derivatives      155Ч157
Lauwerier      xi 349 350
Le Caine      54
Legendre polynomials      45 47 71 72
Leibnitz      155 434
Lew      54
Liouville      v xi 285 287 288 292 294 316 321 323
Liouville-Green method      285Ч321 323
Logarithm of factorial      37 54 105Ч106 435Ч436 448
Logarithmic derivative of factorial function      29 31 41Ч42 72Ч73 78Ч79 89Ч91 93Ч94 105Ч106 435^36 448
Lohmander      224 254 264 274
Lommel function of two variables      80 108 109 215 378Ч381 391Ч394 399 400 442Ч444 450Ч451
Lommel polynomials      46 47
Longer      286 294 295 317 321 349
Macdonald      224 254
MacFarlane      403 430
Maclaurin      v xi
MacRobert      54
Magnus      54
Malaviya      x
Malmsten      66 99 105 106
Many-valued functions      12 148
Mapping      247
Maslov      321
Mathews      54
Mathieu functions      x 17 277 .117
McDougall      55
McGill      x
Meijer      55
Meissel      vi xi
Mellin transforms      27 30 48 53 223 231 239Ч240 278 331Ч334 363Ч366 371 428
Miller      vi xi 404 408 430
Milne-Thomson      335 350
Mittag-Leffler      38 55
Modified Bessel function      36 50 51 54 62Ч65 78 86 95Ч96 104Ч105 108 181Ч182 189 201 212 240 281Ч282 440Ч441 451
Modified Lommel function of two variables      381 451
Modified Struve function      79 80 371Ч376 381 389Ч391 445Ч446
Modifying factor      431Ч434
mount      14 24
Multivalued functions      12 148
Muravev      215
Murnaghan      408 430
Mutter      x xi
Neumann Ч Lommel polynomials      46
Neutralizer      132
Nevanlinna      430
Newton series      216 258 433 451
Ng      vii xi
Nicholson      248
Nielsen      54
Nikiforov      321
Ninham      140 154
Non-linear phase-integral method      322Ч330 495Ч496
Non-numerical compliance definition of an asymptotic expansion      19Ч21 30 35
Norlund      335 336 350
Numerical analysis      411
Oberhettinger      54 55
Olver      vi x xi 20 134 139 248 292 317 321 349
Optics      14
Ott      263 274
Overlapping contributions from expansion points      ix 131Ч132 141
Pade sequences      15 403
Parabolic cylinder functions      8Ч12 203Ч204 224 258 283 319Ч320 329Ч330 349 449 486Ч487 498
Partial sum of asymptotic series      401
Pearson      54
Perturbation expansions      vii
Phase convention for fractional powers      12Ч13
Phase-integral methods      8 10 14 285Ч350 362 489Ч498
Physics      vii 13 14 277
Placzek      54 130
Poincare      v xi 16 25
Poincare Ч Watson definition of an asymptotic power series      17Ч19 28 30 101
PoincareТs definition of an asymptotic power series      v 16Ч17 294Ч295
Poiseuille functions      349
poisson      63
Polynomial form of recurrence relation      296 353 384
Principal value of an integral      412
Psi function      29 31 41Ч42 72Ч73 78Ч79 89Ч91 93Ч94 105Ч106 435Ч436 448
Quadratic contours      135Ч136
quantum mechanics      11 14 318
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