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Zhang S., Jin J. — Computation of Special Functions
Zhang S., Jin J. — Computation of Special Functions

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Название: Computation of Special Functions

Авторы: Zhang S., Jin J.

Аннотация:

Deals with the automatic computation of special functions which appear in all areas of engineering and the physical sciences. Contains over 100 computer programs written by the authors and describes the algorithms to provide readers with specific information about each individual program. Consisting of three sections, the first one presents an introduction to the special function to be dealt with, its major properties, and several formulas needed for its computation. The second segment features algorithms for computing the special function and the related quantities and lists corresponding Fortran-77 programs. The final part tabulates representative results to offer a quick outlook on the function's behavior and to check the computed results. The accompanying disk contains all the computer programs discussed in the text.


Язык: en

Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 717

Добавлена в каталог: 31.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Airy functions      325—340
Airy functions, curves      326 327
Airy functions, differential equation      325
Airy functions, integral of      329 333
Airy functions, numerical computation      329—336
Airy functions, relation with Bessel functions      327 328
Airy functions, tables      337 338
Airy functions, zeros      339
Airy's equation      325
Arithmetic-geometric mean method for complementary elliptic integrals      664
Arithmetic-geometric mean method for elliptic integrals      663
Arithmetic-geometric mean method for Jacobian elliptic functions      671
Associated Legendre functions, arbitrary degree      104—112
Associated Legendre functions, arbitrary degree, curves      105—107
Associated Legendre functions, arbitrary degree, definition      104 105
Associated Legendre functions, arbitrary degree, numerical computation      108
Associated Legendre functions, arbitrary degree, recurrence relations      108
Associated Legendre functions, arbitrary degree, special values      107
Associated Legendre functions, arbitrary degree, tables      122 123
Associated Legendre functions, arbitrary degree, zeros      124
Associated Legendre functions, differential equation      77
Associated Legendre functions, first kind      89—96
Associated Legendre functions, first kind, curves      90—92
Associated Legendre functions, first kind, definition      89
Associated Legendre functions, first kind, numerical computation      94
Associated Legendre functions, first kind, orthogonal relations      93
Associated Legendre functions, first kind, recurrence relations      93 94
Associated Legendre functions, first kind, special values      92
Associated Legendre functions, first kind, symmetry relations      93
Associated Legendre functions, first kind, tables      118 119
Associated Legendre functions, second kind      96—104
Associated Legendre functions, second kind, curves      98—100
Associated Legendre functions, second kind, definition      96
Associated Legendre functions, second kind, numerical computation      101
Associated Legendre functions, second kind, recurrence relations      100
Associated Legendre functions, second kind, special values      98
Associated Legendre functions, second kind, symmetry relations      100
Associated Legendre functions, second kind, tables      120 121
Associated Legendre functions, Wronskian relation      101
Associated Legendre polynomials      78 89
Associated Legendre polynomials, tables      118 119
Bernoulli numbers      1—6
Bernoulli numbers, numerical calculation      5
Bernoulli numbers, recurrence relation      1
Bernoulli numbers, table      10
Bernoulli polynomials      1 2
Bernoulli polynomials, generating function      1
Bessel functions      126—201
Bessel functions, asymptotic expansions      131
Bessel functions, curves      128 129
Bessel functions, differential equation      126
Bessel functions, integral of      252—260
Bessel functions, integral of, asymptotic expressions      253 257
Bessel functions, integral of, curves      269
Bessel functions, integral of, numerical computation      254—256 258—260
Bessel functions, integral of, polynomial approximation      255 259
Bessel functions, integral of, series expansions      253 257
Bessel functions, integral of, table      270
Bessel functions, integral representation      41
Bessel functions, large-argument approximation      128
Bessel functions, large-order asymptotic expressions      172
Bessel functions, negative arguments      149
Bessel functions, negative orders      162
Bessel functions, Neumann series      177
Bessel functions, normalization relations      131
Bessel functions, numerical computation, arbitrary orders      161—175
Bessel functions, numerical computation, complex arguments      149—161
Bessel functions, numerical computation, real arguments      140—148
Bessel functions, numerical computation, zeroth and first orders      131—140
Bessel functions, polynomial approximation      137
Bessel functions, recurrence relations      130
Bessel functions, series expansions      131
Bessel functions, small-argument approximation      128
Bessel functions, tables      185—196
Bessel functions, Wronskian relations      130 157 172 178
Bessel functions, zeros      180—182
Bessel functions, zeros, tables      196—200
Bessel's equation      126
beta function      53—55
Beta function, integral representation      40
Beta function, recurrence relations      54
Chebyshev polynomials      13—18
Chebyshev polynomials, curves      15 16
Chebyshev polynomials, first kind      14
Chebyshev polynomials, Fourier series      17
Chebyshev polynomials, generation function      14
Chebyshev polynomials, numerical computation      23
Chebyshev polynomials, orthogonal relations      17
Chebyshev polynomials, recurrence relations      17
Chebyshev polynomials, reflection formulas      17
Chebyshev polynomials, Rodrigues's formulas      14
Chebyshev polynomials, second kind      14
Chebyshev polynomials, special values      16
Chebyshev polynomials, table      25
Chebyshev's equation, first kind      13
Chebyshev's equation, second kind      14
Confluent hypergeometric equation      385
Confluent hypergeometric functions      385—411
Confluent hypergeometric functions, asymptotic formulas      388
Confluent hypergeometric functions, curves      389—393
Confluent hypergeometric functions, differentiation formulas      387
Confluent hypergeometric functions, integral representation      42
Confluent hypergeometric functions, numerical computation      398
Confluent hypergeometric functions, recurrence relations      389
Confluent hypergeometric functions, series expansion      386 388
Confluent hypergeometric functions, special values      387
Confluent hypergeometric functions, tables      412—423
Confluent hypergeometric functions, transformation formulas      387
Confluent hypergeometric functions, Wronskian relations      387
Cosine integral      644—653
Cosine integral, asymptotic expansion      647
Cosine integral, curve      645
Cosine integral, numerical computation      647
Cosine integral, polynomial approximation      649
Cosine integral, rational approximation      649
Cosine integral, series expansion      646
Cosine integral, table      652
Elliptic cylinder functions      475
Elliptic functions      see "Jacobian elliptic functions"
Elliptic integrals      654—666
Elliptic integrals, arithmetic-geometric mean method      663
Elliptic integrals, complementary      656
Elliptic integrals, complete      655
Elliptic integrals, curves      656—659
Elliptic integrals, numerical computation      661 665
Elliptic integrals, polynomial approximation      661
Elliptic integrals, series expansions      659
Elliptic integrals, tables      673—677
Error function      620—624
Error function, asymptotic expansion      621
Error function, curve      622
Error function, numerical computation      621
Error function, polynomial approximation      622
Error function, series expansion      621
Error function, tables      637 638
Error function, zeros      635 642
Euler integral, first kind      53
Euler integral, second kind      44
Euler numbers      6—9
Euler numbers, numerical calculation      8
Euler numbers, recurrence relation      6
Euler numbers, table      10
Euler polynomials      6 7
Euler polynomials, generating function      6
Euler's constant      45
Exponential integrals      680—693
Exponential integrals, asymptotic expansions      682
Exponential integrals, continued fraction      683
Exponential integrals, curves      681 682
Exponential integrals, numerical computation      684
Exponential integrals, rational approximations      683
Exponential integrals, recurrence relation      681
Exponential integrals, series expansions      682
Exponential integrals, tables      689—692
Fourier — Chebyshev series      17
Fourier — Hermite series      22
Fourier — Laguerre series      20
Fourier — Legendre series      81—94
Fresnel integrals      625—636
Fresnel integrals, asymptotic expansions      630
Fresnel integrals, curves      627 628
Fresnel integrals, modified      626
Fresnel integrals, numerical computation      630
Fresnel integrals, series expansions      629
Fresnel integrals, symmetry relations      629
Fresnel integrals, tables      639—641
Fresnel integrals, zeros      635 642
Gamma function      44—53
Gamma function, asymptotic expansion      48
Gamma function, curves      45
Gamma function, integral representation      40
Gamma function, multiplication formulas      47
Gamma function, numerical computation      49
Gamma function, recurrence relations      46
Gamma function, reflection formulas      47
Gamma function, series expansion      47
Gamma function, Stirling's formulas      49
Gamma function, tables      67—71
Gauss's equation      366
Gaussian probability integral      624
Gaussian probability integral, polynomial approximation      625
Gaussian quadrature      28
Gaussian quadrature, Gauss — Chebyshev quadrature      32
Gaussian quadrature, Gauss — Hermite quadrature      37
Gaussian quadrature, Gauss — Laguerre quadrature      32
Gaussian quadrature, Gauss — Legendre quadrature      28
Generating function for Bernoulli polynomial      1
Generating function for Chebyshev polynomial      14
Generating function for Euler polynomial      6
Generating function for Hermite polynomial      21
Generating function for Laguerre polynomial      18
Hankel functions      127
Hankel functions, large-argument approximation      129
Hankel functions, numerical computation      235—239
Hankel functions, spherical      274
Helmholtz equation      697
Hermite polynomials      20—23
Hermite polynomials, curves      22
Hermite polynomials, Fourier series      22
Hermite polynomials, generating function      21
Hermite polynomials, numerical computation      23
Hermite polynomials, orthogonal relation      22
Hermite polynomials, recurrence relation      22
Hermite polynomials, Rodrigues's formula      21
Hermite polynomials, special values      21
Hermite polynomials, symmetry relation      22
Hermite polynomials, table      27
Hermite's equation      21
Hypergeometric equation      366
Hypergeometric functions      366—385
Hypergeometric functions, asymptotic formula      369
Hypergeometric functions, differentiation formulas      368
Hypergeometric functions, integral representation      41
Hypergeometric functions, numerical computation      374
Hypergeometric functions, recurrence relations      372
Hypergeometric functions, series expansion      367
Hypergeometric functions, special values      368
Hypergeometric functions, transformation formulas      369
Incomplete beta function      64—66
Incomplete beta function, continued fraction      65
Incomplete beta function, curves      64
Incomplete beta function, integral representation      40
Incomplete beta function, numerical computation      66
Incomplete beta function, recurrence relations      65
Incomplete beta function, series expansion      65
Incomplete beta function, tables      75
Incomplete gamma function      61—64
Incomplete gamma function, asymptotic expression      62
Incomplete gamma function, continued fraction      63
Incomplete gamma function, curves      61 62
Incomplete gamma function, numerical computation      63
Incomplete gamma function, recurrence relations      62
Incomplete gamma function, series expansion      62
Incomplete gamma function, tables      74
Jacobian elliptic functions      666—672
Jacobian elliptic functions, arithmetic-geometric mean method      671
Jacobian elliptic functions, basic formulas      667 669
Jacobian elliptic functions, curves      668
Jacobian elliptic functions, numerical computation      670
Jacobian elliptic functions, series expansion      670
Jacobian elliptic functions, tables      678
Kelvin functions      307—324
Kelvin functions, asymptotic expansion      312
Kelvin functions, curves      311
Kelvin functions, differential equation      307
Kelvin functions, negative arguments      311
Kelvin functions, negative orders      311
Kelvin functions, numerical computation      315—320
Kelvin functions, polynomial approximation      318
Kelvin functions, recurrence relations      311
Kelvin functions, series expression      308
Kelvin functions, special values      311
Kelvin functions, tables      322 323
Kelvin functions, zeros      321
Kelvin's equation      307
Kummer's equation      385
Kummer's transformation formulas      387
Laguerre polynomials      18—20
Laguerre polynomials, curves      19
Laguerre polynomials, Fourier series      20
Laguerre polynomials, generating function      18
Laguerre polynomials, numerical computation      23
Laguerre polynomials, orthogonal relation      20
Laguerre polynomials, recurrence relations      20
Laguerre polynomials, Rodrigues's formula      18
Laguerre polynomials, special values      20
Laguerre polynomials, table      26
Laguerre's equation      18
Lambda functions      182—184
Lambda functions, curves      183
Lambda functions, differential equation      182
Lambda functions, recurrence relation      183
Lambda functions, series expansion      182
Legendre functions      77—125
Legendre functions, arbitrary degree      104
Legendre functions, differential equation      78
Legendre functions, first kind      78—83
Legendre functions, first kind, curves      79 80
Legendre functions, first kind, definition      78
Legendre functions, first kind, integral of      82
Legendre functions, first kind, numerical computation      81
Legendre functions, first kind, orthogonal relations      80
Legendre functions, first kind, recurrence relations      80
Legendre functions, first kind, Rodrigues's formula      78
Legendre functions, first kind, special values      79
Legendre functions, first kind, symmetry relations      80
Legendre functions, second kind      83—89
Legendre functions, second kind, curves      84 85
Legendre functions, second kind, definition      83
Legendre functions, second kind, numerical computation      86
Legendre functions, second kind, recurrence relations      85
Legendre functions, second kind, special values      84
Legendre functions, second kind, symmetry relations      85
Legendre functions, tables      116 117
Legendre functions, Wronskian relation      86
Legendre polynomials      78
Legendre polynomials, tables      114 115
Legendre's equation      78
Mathieu functions      475—535
Mathieu functions, characteristic values      479
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