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| Ïîèñê ïî óêàçàòåëÿì |
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| Olver F.W.J. — Asymptotics and Special Functions |
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| Ïðåäìåòíûé óêàçàòåëü |
Moore, W. K. 336
Moriguchi, H. 366
Morse, P. M. 501
Mott, N. F. 433
Muckenhoupt, B. 446
Muldoon, M. E. 338 434
Murnaghan, F. D. 544
Nakano, M. 517
National Bureau of Standards (N.B.S.) 64 168 277 282 321 526 543
National Physical Laboratory (N.P.L.) 541
Natterer, F 228
Navot, I. 321
Nayfeh, A. H. 433 434
Newton, R. G. 479
Ng, E. W. 64
Nicolaenko, B. 317
Ninham, B. W. 321
Nishimoto, T. 517
Norlund, N. E. 282
Nosova, L. N. 434
Oberhettinger, F. 278 321 361
Olver, F. W. J. 76 92 94 104 105 109 112 136 137 138 228 250 266 269 276 277 278 302 313 315 334 373 381 391 405 413 416 418 433 434 462 477 478 479 496 517 518
Order relations 4—11 29
Order relations, implied constants 5 7
Orthogonal polynomials 46—48 65 Jacobi Laguerre Legendre
Orthogonal polynomials, Christoffel — Darboux formula 48
Orthogonal polynomials, classical 48—52
Orthogonal polynomials, differential equations for 50 52
Orthogonal polynomials, generating functions 51 52
Orthogonal polynomials, Gram — Schmidt process 47
Orthogonal polynomials, normalization 46 47
Orthogonal polynomials, recurrence relations 47 50 52
Orthogonal polynomials, Rodrigues’ formulas 49
Orthogonal polynomials, zeros 47
Orthonormal polynomials 46
Papperitz equation 157
Parabolic cylinder functions 206—207 (see also “Weber’s differential equation”)
Parabolic cylinder functions of large order 207—208 228 334
Parabolic cylinder functions, integral representation 208
Parabolic cylinder functions, notation 207 228
Parabolic cylinder functions, relation to confluent hypergeometric functions 259
Path 29
Phase function 394 436 456
Phase principle 247—248
Phase principle, example 252—253
Phase shift 210 449—451 479
Phase-integral method 517
Pike, E. R. 228 478 518
Pittnauer, F. 30
Po1ya, G. 105
Pochhammer, L. 38
Pochhammer’s notation  159
Poincare, H. 4 16 27 105
Poisson’s summation formula 306
Pollak, H. O. 309
Potential barrier 501 517—518
Prime numbers 63—64
Principal curves 487 504 518 521
Principal directions 509
Principal subdomains 504
Principle of the argument see “Phase principle”
Progressive paths 222 266 367
Progressive paths, choice of 224—227 508
Proper degree 46
Prym’s function 45
Prym’s function, asymptotic expansion of 295
Prym’s function, Gauss’s formula 40
Psi function 39
Rayleigh (Lord) 228 516
Redheffer, R. M. 31 123 128 146 247
Reflection coefficient 503 515
Region 7
Regular arc 29 147
Regular singularities see “Singularities of differential equations”
Reid, W. H. 368 518
Remainder term 2
Remainder term, optimum 522
Reudink, D. O. J. 251 321
Reversion of series 21 —22 313—315
Riccati equation 192
Rice, S. O. 361
Riedel, R. 361
Riekstina, V. 321
Riekstins, E. 29 30 317 361
Riemann equation 157
Riemann, B. 61 63 64 65 137 157 158
Riemann-Lebesgue lemma 73 99 104
Ritchie, R. H. 44
Ritt, J. R 9 29
Roberts, J. H. 94
Robin, L. 189 479
Rosser, J. B. 542 543
Royal Society (R.S.) 247 278 434
Rubin, R, J. 329
Sabatier, P. C 479
Saddle point 126 136
Saddle point, coinciding with pole 130 528
Saddle-point method 138
Saw-tooth function 279
Scattering theory 208 433 449
Schindler, S. 479
Schlesinger, L. 391
Schmidt, H. 30
Schoenfeld, L. 329
Schrodinger equation 449
Schwarzian derivative 191
Schwarz’s principle of symmetry 128
Scorer, R. S. 431
Scorer’s functions 332 430—432 434
Sectional continuity 73
Semiconvergent series 3
Shadow zones 223—224 417
Shadow zones, necessity of 236
Shanks, D. 544
Shepp, L. 309
Sibuya, Y. 277
Sine integrals 41—43
Sine integrals, asymptotic expansion of 67 320
Sine integrals, Laplace transform of 43
Singularities of differential equations 148 (see also “Differential equations Irregular LG
Singularities of differential equations at infinity 153—154
Singularities of differential equations, connection formulas at 480—482
Singularities of differential equations, expansions at 148—150 153
| Singularities of differential equations, exponents 149 153 482
Singularities of differential equations, exponents differing by integer 150—152
Singularities of differential equations, indices 149
Singularities of differential equations, indicial equation 149
Singularities of differential equations, numerically satisfactory solutions at 154—155
Singularities of differential equations, rank 148 154
Singularities of differential equations, regular 148 153
Singularity, extraction of singular part 120
Skovgaard, H. 412 446
Slater, L. J. 189 277 278
Slowly convergent series 544
Snow, C 189
Soni, K. 361
Soni, R. P. 361
Spira, R. 294
Stationary phase see “Method of stationary phase”
Stationary points 96
Staton, J. 44
Steepest descents see “Method of steepest descents”
Steffensen, J. F. 69
Steinig, J. 278
Stenger, F. 278 361 391
Stieltjes transform 92
Stieltjes, T. J. 294 543
Stirling’s formula 88
Stirling’s series 293—295
Stokes lines 518 521
Stokes, G. G. 105 240 518 543
Stokes’ phenomenon 240
Struve’s equation 274
Struve’s equation, numerically satisfactory solutions 276—277
Struve’s function 275—277 278
Successive approximations, method of 141
Summation by parts 296 540
Sums of powers of integers 283 284 292
Swanson, C. A. 412 446 478
Sweeney, D. W. 64
Szego, P. 434
Szego.G. 65 105 137 479
Tail of power series 7
Taylor coefficients, asymptotic expansion of 309—315 329—331
Tetragamma function 39
Thome, L. W. 230
Thorne, R. C 223 391
Thurber, J. K. 317
Titchmarsh, E. C. 26 54 65 161 306 498
Tolstov, G. P. 315
Total variation see “Variation”
Transcendental equations, asymptotic solution of complex variables 14—16 29
Transcendental equations, asymptotic solution of real variables 11—14 29
Transition points 192 362 474
Transmission coefficient 503 515
Tricomi, F. O. 120 278
Trigamma function 39
Truncation error 2
Tumarkin, S. A. 434
Turning points 192 398
Turning points, multiple 363 474—478
Turning-point problems see “Connection formulas”
Turning-point problems, asymptotic solutions for complex variables 416—419
Turning-point problems, asymptotic solutions for real variables 397—401 408—413 426—429
Turning-point problems, coefficients in asymptotic solutions 409—410 412—413 419
Turning-point problems, error bounds for asymptotic solutions 399—400 410 417—418
Turning-point problems, first approximation 397—400
Turning-point problems, formal series solutions 409 427—428
Turning-point problems, history 433 516—517
Turning-point problems, inhomogeneous equations 429—430 434
Turning-point problems, more general form 426—429 474—478
Turning-point problems, stationary values of solutions 408
Turning-point problems, zeros of solutions 405—408
Turrittin, H. L. 391 433
Ursell, F. 137 351 358 361
van der Corput, J. G. 27 29 68 105
van der Waerden, B. L. 361
van Wijngaarden, A. 544
Variation 27—29
Variation of negative power 225—227
Variation, convergence at singularity 200—202
Variational operator 27
Wainger, S. 446
Wasow, W. 278 391 433 517
Watson, G. N. 30 64 71 105 153 162 189 228 245 249 254 268 269 277 278 294 313 315 321 340 342 438 444 543 544
Watson’s lemma for loop integrals 120
Watson’s lemma, complex variables 112—113
Watson’s lemma, error bounds for 89—90 105 114—116
Watson’s lemma, estimation of remainder term 544
Watson’s lemma, history 104
Watson’s lemma, real variables 71
Wave penetration 501 513 517—518
Weber parabolic cylinder functions see “Parabolic cylinder functions”
Weber, H. F. 103
Weber’s differential equation 147 206
Weber’s differential equation, connection formulas for solutions 516
Weber’s differential equation, zeros of solutions 214
Weber’s function  103
Weber’s function  242 (see also “Bessel functions”)
Weight functions 46 394 415 437 454
Wentzel, G. 228
Whittaker functions 260 (see also “Confluent hypergeometric functions Whittaker’s
Whittaker functions of large argument 260 266
Whittaker functions with large k 412 446—447
Whittaker functions with large m 260—261 278 368 401—402
Whittaker functions, zeros 452—453
Whittaker, E. T. 64 153 189 207 294 321
Whittaker’s equation 260
Whittaker’s equation, connection formulas for solutions 261 262 516
Widder, D. V. 68 105
Wilkins, J. E. 340
WKB approximation see “LG approximation”
WKB or WKBJ method 228 517
Wong, R. 104 317
Wrench, J. W., Jr. 88 544
Wright, E. M. 321
wronskian 142
Wyman, M. 30 104 138 317 321
Wynn, P. 543 544
Zeros, asymptotic approximations from LG approximation 211—214 228
Zeros, asymptotic approximations in Case III 451—453
Zeros, asymptotic approximations in turning-point problems 405—408
Zeta function 61—64 65
Zeta function of integer argument 63 283
Zeta function, Jensen’s formula 292
Zwaan, A. 517
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