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| Авторизация |
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| Поиск по указателям |
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| Zhang S., Jin J. — Computation of Special Functions |
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| Предметный указатель |
Mathieu functions, characteristic values, approximation 482
Mathieu functions, characteristic values, curves 482
Mathieu functions, characteristic values, numerical computation 501
Mathieu functions, characteristic values, tables 521—524
Mathieu functions, curves 488
Mathieu functions, definition 475
Mathieu functions, expansion coefficients 477
Mathieu functions, expansion coefficients, normalization relations 477 478
Mathieu functions, expansion coefficients, numerical computation 512
Mathieu functions, expansion coefficients, recurrence relations 477 478
Mathieu functions, expansion coefficients, tables 525 526
Mathieu functions, expansion of 485
Mathieu functions, Fourier series expansion 476
Mathieu functions, normalization relation 477
Mathieu functions, numerical computation 501 516
Mathieu functions, orthogonal relations 489
Mathieu functions, periodicity 476 487
Mathieu functions, special values 487
Mathieu functions, symmetry 487
Mathieu functions, tables 527 528
Mathieu functions, zeros 533
Mathieu — Hankel functions 495
Miller's method 695
Modified Bessel functions 202—251
Modified Bessel functions, curves 204—205
Modified Bessel functions, differential equation 202
Modified Bessel functions, first kind 202
Modified Bessel functions, integral of 261—268
Modified Bessel functions, integral of, asymptotic expressions 261 265
Modified Bessel functions, integral of, curves 269
Modified Bessel functions, integral of, numerical computation 262—264 266—268
Modified Bessel functions, integral of, polynomial approximation 263 267
Modified Bessel functions, integral of, series expansions 261 265
Modified Bessel functions, integral of, table 271
Modified Bessel functions, integral representation 41
Modified Bessel functions, large-argument approximation 205
Modified Bessel functions, large-argument asymptotic expansion 207
Modified Bessel functions, large-order approximation 205
Modified Bessel functions, large-order asymptotic expansion 234
Modified Bessel functions, negative arguments 218
Modified Bessel functions, negative orders 226
Modified Bessel functions, Neumann series 206
Modified Bessel functions, numerical computation, arbitrary orders 225—233
Modified Bessel functions, numerical computation, complex arguments 217—225
Modified Bessel functions, numerical computation, real arguments 213—217
Modified Bessel functions, numerical computation, zeroth and first orders 207—212
Modified Bessel functions, polynomial approximation 210
Modified Bessel functions, recurrence relations 206
Modified Bessel functions, second kind 203
Modified Bessel functions, small-argument approximation 204
Modified Bessel functions, tables 240—250
Modified Bessel functions, Wronskian relations 206 220 233
Modified Bessel's equation 202
Modified Mathieu functions 489—500
Modified Mathieu functions, curves 497—500
Modified Mathieu functions, definition 489
Modified Mathieu functions, numerical computation 501 516
Modified Mathieu functions, tables 529—532
Modified Mathieu functions, Wronskian relation 496
Modified Mathieu functions, zeros 534
Modified Newton's method 705
Modified spherical Bessel functions 286—294
Modified spherical Bessel functions, curves 290
Modified spherical Bessel functions, differential equation 286
Modified spherical Bessel functions, numerical computation 291—294
Modified spherical Bessel functions, Rayleigh formula 288
Modified spherical Bessel functions, recurrence relations 289 290
Modified spherical Bessel functions, series expressions 287 288
Modified spherical Bessel functions, small-argument approximation 289
Modified spherical Bessel functions, tables 302—305
Modified spherical Bessel functions, Wronskian relation 290 293
Modified spherical Bessel's equation 286
Modified Struve functions 353—362
Modified Struve functions, asymptotic expansions 357
Modified Struve functions, curves 354—355
Modified Struve functions, integrals of 356 357 361
Modified Struve functions, numerical computation 357—362
Modified Struve functions, recurrence relations 356
Modified Struve functions, series expression 353
Modified Struve functions, table 364
Newton's method 704
Newton's method, modified 705
Orthogonal polynomials 12—43
Orthogonal polynomials, numerical computation 23
Parabolic cylinder functions 425—474
Parabolic cylinder functions, asymptotic expansions 437
Parabolic cylinder functions, basic properties 432
Parabolic cylinder functions, curves 429—434
Parabolic cylinder functions, definitions 428
Parabolic cylinder functions, numerical computation 438
Parabolic cylinder functions, orthogonal relations 436
Parabolic cylinder functions, recurrence relations 435
Parabolic cylinder functions, series expansions 437
Parabolic cylinder functions, tables 456—467 470—473
Parabolic cylinder functions, Wronskian relations 436
Parabolic cylinder functions, zeros 468 469
Probability integral 624
| Probability integral, polynomial approximation 625
Psi function 56—61
Psi function, asymptotic expansion 58
Psi function, curves 57
Psi function, duplication formula 57
Psi function, numerical computation 58
Psi function, recurrence relations 57
Psi function, reflection formulation 57
Psi function, series expression 56
Psi function, special values 56
Psi function, tables 72 73
Riccati — Bessel functions 283—286
Riccati — Bessel functions, curves 283 284
Riccati — Bessel functions, differential equation 283
Riccati — Bessel functions, numerical computation 284—286
Riccati — Bessel functions, tables 300 301
Rodrigues's formulas for Chebyshev polynomials 14
Rodrigues's formulas for Hermite polynomials 21
Rodrigues's formulas for Laguerre polynomials 18
Rodrigues's formulas for Legendre polynomials 78
Separation of variable, method of 698
Sine integral 644—653
Sine integral, asymptotic expansion 647
Sine integral, curve 645
Sine integral, numerical computation 647
Sine integral, polynomial approximation 649
Sine integral, rational approximation 649
Sine integral, series expansion 646
Sine integral, table 652
Spherical Bessel functions 273—283
Spherical Bessel functions, curves 277
Spherical Bessel functions, differential equation 273
Spherical Bessel functions, large-argument approximation 276
Spherical Bessel functions, negative arguments 282
Spherical Bessel functions, negative orders 283
Spherical Bessel functions, numerical computation 278—282
Spherical Bessel functions, Rayleigh formula 275
Spherical Bessel functions, recurrence relations 278
Spherical Bessel functions, series expressions 274
Spherical Bessel functions, small-argument approximation 276
Spherical Bessel functions, tables 296—299
Spherical Bessel functions, Wronskian relation 278 281
Spherical Bessel's equation 273
Spherical Hankel functions 274
Spherical Hankel functions, closed-form expressions 276
Spheroidal coordinates 536—540
Spheroidal coordinates, oblate 538
Spheroidal coordinates, prolate 536
Spheroidal wave functions 536—619
Spheroidal wave functions, numerical computation 569—594
Spheroidal wave functions, numerical computation, angular functions 578
Spheroidal wave functions, numerical computation, characteristic values 570
Spheroidal wave functions, numerical computation, expansion coefficients 572
Spheroidal wave functions, numerical computation, oblate radial functions 589
Spheroidal wave functions, numerical computation, prolate radial functions 580
Spheroidal wave functions, oblate 559—569
Spheroidal wave functions, oblate, curves 560—566
Spheroidal wave functions, oblate, evaluation 567
Spheroidal wave functions, oblate, joining factor 561
Spheroidal wave functions, oblate, Wronskian relation 567
Spheroidal wave functions, prolate 542—558
Spheroidal wave functions, prolate, characteristic values 550 552
Spheroidal wave functions, prolate, curves 544—549
Spheroidal wave functions, prolate, evaluation 556
Spheroidal wave functions, prolate, expansion coefficients 550 555
Spheroidal wave functions, prolate, joining factor 549
Spheroidal wave functions, prolate, orthogonal relation 543
Spheroidal wave functions, prolate, Wronskian relation 546
Spheroidal wave functions, tables 595—618
Spheroidal wave functions, tables, characteristic values 595—598 607—610
Spheroidal wave functions, tables, oblate angular functions 611 612
Spheroidal wave functions, tables, oblate radial functions 613—618
Spheroidal wave functions, tables, prolate angular functions 599 600
Spheroidal wave functions, tables, prolate radial functions 601—606
Struve functions 341—353
Struve functions, asymptotic expansions 345
Struve functions, curves 342 343
Struve functions, differential equation 341
Struve functions, integrals of 345 346 351
Struve functions, numerical computation 346—353
Struve functions, recurrence relations 344
Struve functions, series expression 342
Struve functions, table 363
Weber parabolic cylinder functions 425
Whittaker functions 395
Whittaker functions, integral representation 42
Whittaker's equation 395
Wronskian relations for associated Legendre functions 101
Wronskian relations for Bessel functions 130 157 172 178
Wronskian relations for confluent hypergeometric functions 387
Wronskian relations for Legendre functions 86
Wronskian relations for modified Bessel functions 206 220 233
Wronskian relations for modified Mathieu functions 496
Wronskian relations for modified spherical Bessel functions 290 293
Wronskian relations for oblate spheroidal wave functions 567
Wronskian relations for parabolic cylinder functions 436
Wronskian relations for prolate spheroidal wave functions 546
Wronskian relations for spherical Bessel functions 278 281
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