Abramowitz M., Stegun I. — Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables :: Электронная библиотека попечительского совета мехмата МГУ

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Abramowitz M., Stegun I. — Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables

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Название: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables

Авторы: Abramowitz M., Stegun I.

Аннотация:

The present volume is an outgrowth of a Conference on Mathematical Tables held at Cambridge, Mass., on September 15-16, 1954, under the auspices of the National Science Foundation and the Massachusetts InstiInstitute of Technology. The purpose of the meeting was to evaluate the need for mathematical tables in the light of the availability of large scale computing machines. It was the consensus of opinion that in spite of the increasing use of the new machines the basic need for tables would continue to exist.

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Рубрика: Математика/Справочники/

Статус предметного указателя: Готов указатель с номерами страниц

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Издание: 10th edition

Год издания: 1972

Количество страниц: 1046

Добавлена в каталог: 30.04.2005

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Предметный указатель

Adam’s formulas      896
Airy functions      367 446 510 540 689
Airy functions and their derivatives      446
Airy functions and their derivatives zeros and associated values of      478
Airy functions ascending series for      446
Airy functions ascending series for integrals of      447
Airy functions asymptotic expansions of      448
Airy functions asymptotic expansions of modulus and phase      449
Airy functions asymptotic forms of integrals of      449
Airy functions asymptotic forms of related functions      450
Airy functions complex zeros and associated values of Bi (z) and Bi’(z)      478
Airy functions computation of      454
Airy functions computation of zeros of      454
Airy functions definitions      446
Airy functions differential equations      446 448
Airy functions graphs of      446
Airy functions integral representations of      447
Airy functions integrals involving      448
Airy functions modulus and phase      449
Airy functions related functions      448
Airy functions relations between      446
Airy functions representations in terms of Bessel functions      447
Airy functions tables of      475
Airy functions tables of integrals of      478
Airy functions Wronskian for products of      448
Airy functions Wronskian relations      446
Airy functions zeros and their asymptotic expansions      450
Airy integrals      447
Aitken’s $\delta^2$ -process      18
Aitken’s iteration method      879
Anger’s function      498
Anger’s function relation to Weber’s function      498
Antilogarithm      89
Approximate values      14
Approximation methods      18
Approximation methods Aitken’s $\delta^2$ -process      18
Approximation methods Newton’s method      18
Approximation methods regula falsi      18
Approximation methods successive substitution      18
Argument      16
Arithmetic functions      826
Arithmetic functions table of      840
Arithmetic mean      10
Arithmetic progression      10
Arithmetic-geometric mean      571 577 578 580 598 601
Associated Legendre functions      331 (see “Legendre functions”)
Asymptotic expansions      15
Basic numbers      822
Bateman function      510
Bernoulli numbers      804
Bernoulli numbers table of      810
Bernoulli polynomials      803
Bernoulli polynomials as sums of powers      804
Bernoulli polynomials coefficients of r      809
Bernoulli polynomials derivatives of      804
Bernoulli polynomials differences of      804
Bernoulli polynomials expansions of      804
Bernoulli polynomials Fourier expansions of      805
Bernoulli polynomials generating function for      804
Bernoulli polynomials inequalities for      805
Bernoulli polynomials integrals involving      805
Bernoulli polynomials multiplication theorem for      804
Bernoulli polynomials relations with Euler polynomials      806
Bernoulli polynomials special values of      805
Bernoulli polynomials symbolic operations      806
Bernoulli polynomials symmetry relations      804
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$       358 379 381 385
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ graphs of      359 373
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ in terms of hypergeometric functions      362
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ notation      358
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ zeros of      370
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ zeros of cross products of      374
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ zeros, complex      372
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ zeros, infinite products for      370
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ zeros, McMahon’s expansions for      371
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ zeros, tables of      371 409 414
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ zeros, uniform expansions of      371
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ , addition theorems for      363
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ , analytic continuation of      361
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ , ascending series for      360
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ , asymptotic expansion for large arguments      364
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ , asymptotic expansions for large orders      365
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ , asymptotic expansions for zeros      371
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ , asymptotic expansions in the transition region for large orders      367
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ , asymptotic expansions of modulus and phase for large arguments      365
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ , connection with Legendre functions      362
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ , continued fractions for      363
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ , derivatives with respect to order      362
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ , differential equation      358
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ , differential equations for products      362
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ , formulas for derivatives      361
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ , generating function and associated series      361
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ , integral representations of      360
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ , limiting forms for small arguments      360
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ , modulus and phase      365
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ , multiplication theorem for      363
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ , Neumann’s expansion of an arbitrary function      363
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ , other differential equations      362
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ , polynomial approximations      369
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ , recurrence relations      361
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ , recurrence relations for cross-products      361
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ , relations between      358
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ , tables of      390
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ , uniform asymptotic expansions for large orders      358
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ , upper bounds      362
Bessel functions $J_{\nu}(z),Y_{\nu}(z)$ , Wronskian relations      360
Bessel functions as parabolic cylinder functions      692 697
Bessel functions definite integrals      485
Bessel functions modified      374 509
Bessel functions notation for      358
Bessel functions of fractional order      437
Bessel functions of half-integer order      437 497
Bessel functions of half-integer order zeros and associated values      467
Bessel functions of half-integer order zeros of the derivative and associated values      468
Bessel functions of the first kind      358 509
Bessel functions of the second kind      358 509
Bessel functions of the third kind      358 510
Bessel functions orthogonality properties of      485
Bessel functions representations in terms of Airy functions      447
Bessel functions spherical      437/509
Bessel functions, integrals      479 485
Bessel functions, integrals asymptotic expansions      480 482
Bessel functions, integrals computation of      488
Bessel functions, integrals convolution type      485
Bessel functions, integrals Hankel — Nicholson type      488
Bessel functions, integrals involving products of      484
Bessel functions, integrals polynominal approximations      481 482
Bessel functions, integrals recurrence relations      480 483
Bessel functions, integrals reduction formulas      483
Bessel functions, integrals repeated      482
Bessel functions, integrals simple      480
Bessel functions, integrals tables of      492
Bessel functions, integrals Weber — Schafheitlin type      487
Bessel’s interpolation formula      881
beta function      258
Biharmonic operator      885
Binary scale      1017
Binomial coefficients      10 256 822
Binomial coefficients table of      10 828
Binomial distribution      960
Binomial series      14
Binomial theorem      10
Bivariate normal probability function      936
Bivariate normal probability function computation of      955
Bivariate normal probability function graphs of      937
Bivariate normal probability function special values of      937
Bode’s rule      886
Cartesian form      16
Catalan’s constant      807
Cauchy — Riemann equation      17

Cauchy’s inequality      11
Characteristic function      928
Chebyshev integration      887
Chebyshev integration abscissas for      920
Chebyshev polynomials      486 561 774;
Chebyshev polynomials coefficients for and in terms of      795
Chebyshev polynomials graphs of      778
Chebyshev polynomials values of      795
Chebyshev's inequality      11
Chi-square distribution function computation of      958
Chi-square probability function      940
Chi-square probability function approximations to      941
Chi-square probability function asymptotic expansion      941
Chi-square probability function continued fraction for      941
Chi-square probability function cumulants for      940
Chi-square probability function non-central      942
Chi-square probability function recurrence and differential properties of      941
Chi-square probability function relation to other functions      941
Chi-square probability function relation to the normal distribution      940
Chi-square probability function series expansions for      941
Chi-square probability function statistical properties of      943
Christoffel — Darboux formula      1785
Circular functions      71 91
Circular functions, addition and subtraction of      72
Circular functions, addition formulas for      72
Circular functions, Chebyshev approximations      76
Circular functions, continued fractions for      75
Circular functions, definite integrals      78
Circular functions, DeMoivre’s formula      74
Circular functions, differentiation formulas      77
Circular functions, Euler’s formulas      74
Circular functions, expansion in partial fractions      75
Circular functions, graphs of      72
Circular functions, half-angle formulas      72
Circular functions, indefinite integrals      77
Circular functions, inequalities for      75
Circular functions, infinite products      75
Circular functions, limiting values      75
Circular functions, modulus and phase      74
Circular functions, multiple angle formulas      72
Circular functions, negative angle formulas      72
Circular functions, periodic properties of      72
Circular functions, polynomial approximations      76
Circular functions, products of      72
Circular functions, real and imaginary parts      74
Circular functions, reduction to first quadrant      73
Circular functions, relation to hyperbolic functions      74
Circular functions, relations between      72
Circular functions, series expansions for      74
Circular functions, signs of      73
Circular functions, tables of      142
Circular normal distribution      936
Circular normal distribution, calculation over an offset circle      957
Clausen’s integral      10°5
Clebsch — Gordan coefficients      1006
Cologarithm      89
Combinatorial analysis      822
complex numbers      16
Complex numbers logarithm of      67 90
Complex numbers multiplication and division of      16
Complex numbers powers of      16
Complex numbers roots of      17
Confluent hypergeometric functions      262 298 300 362 377 486 503 686 691 695 780
Confluent hypergeometric functions alternative notations for      504
Confluent hypergeometric functions analytic continuation of      504
Confluent hypergeometric functions asymptotic expansions and limiting forms      508
Confluent hypergeometric functions calculation of zeros and turning points of      513
Confluent hypergeometric functions computation of      511
Confluent hypergeometric functions connections with Bessel functions      506
Confluent hypergeometric functions graph of zeros of      513
Confluent hypergeometric functions graphing of      513
Confluent hypergeometric functions graphs of      514
Confluent hypergeometric functions, Barnes-type contour integrals      506
Confluent hypergeometric functions, differential properties of      506
Confluent hypergeometric functions, expansions in series of Bessel functions      506
Confluent hypergeometric functions, general confluent equation      505
Confluent hypergeometric functions, integral representations of      505
Confluent hypergeometric functions, recurrence relations      506
Confluent hypergeometric functions, Rummer’s equation      504
Confluent hypergeometric functions, Rummer’s functions      504
Confluent hypergeometric functions, Rummer’s transformations      505
Confluent hypergeometric functions, special cases of      509
Confluent hypergeometric functions, table of      516
Confluent hypergeometric functions, table of zeros of      535
Confluent hypergeometric functions, Whittaker’s equation      505
Confluent hypergeometric functions, Whittaker’s functions      505
Confluent hypergeometric functions, Wronskian relations      505
Confluent hypergeometric functions, zeros and turning values      510
Conformal mapping      642
Conical functions      337
Constants mathematical      1
Constants physical, miscellaneous      5
Continued fractions      19 22 68 70 75 81 85 88 229 258 263 298 932 941 944
Conversion factors mathematical      1
Conversion factors physical      5
Cornish — Fisher asymptotic expansions      935
Correlation      936
Cosine integral      231 510
Cosine integral asymptotic expansions of      233
Cosine integral computation of      233
Cosine integral definitions      231
Cosine integral graphs of      232
Cosine integral, integral representation of      232
Cosine integral, integrals involving      232
Cosine integral, rational approximations      233
Cosine integral, relation to the exponential integral      232
Cosine integral, series expansions for      232
Cosine integral, symmetry relations      232
Cosine integral, tables of      238 243
Coulomb wave functions      509 537
Coulomb wave functions, asymptotic behavior of      542
Coulomb wave functions, asymptotic expansions of      540
Coulomb wave functions, computation of      543
Coulomb wave functions, differential equation      538
Coulomb wave functions, expansions in terms of Airy functions      540
Coulomb wave functions, expansions in terms of Bessel — Clifford functions      539
Coulomb wave functions, expansions in terms of spherical Bessel functions      540
Coulomb wave functions, general solution      538
Coulomb wave functions, graphs of      539 541
Coulomb wave functions, integral representations of      539
Coulomb wave functions, recurrence relations      539
Coulomb wave functions, series expansions for      538
Coulomb wave functions, special values of      542
Coulomb wave functions, tables of      546
Coulomb wave functions, Wronskian relations      539
Cubic equation, solution of      17 20
Cumulants      928
Cumulative distribution function multi variate      927
Cumulative distribution function univariate      927
Cunningham function      510
Cylinder functions      361
Dawson’s integral      262 298 305 692
Dawson’s integral graph of      297
Dawson’s integral table of      319
Debye functions      998
DeMoivre’s Theorem      74 84
derivatives      11
Derivatives of algebraic functions      11
Derivatives of circular functions      77
Derivatives of hyperbolic functions      85
Derivatives of inverse circular functions      82
Derivatives of inverse hyperbolic functions      88
Derivatives of logarithmic functions      69
Derivatives partial      883
Differences      877
Differences central      877
Differences divided      877
Differences forward      877
Differences in terms of derivatives      883
Differences mean      877

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