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

Spherical Bessel functions, ascending series for      437
Spherical Bessel functions, complex zeros of $h^{(1)}_n(z), h^{(2)}_n(z)$       441
Spherical Bessel functions, computation of      452
Spherical Bessel functions, cross products of      439
Spherical Bessel functions, definitions      437
Spherical Bessel functions, degenerate forms      440
Spherical Bessel functions, derivatives with respect to order      440
Spherical Bessel functions, differential equation      437
Spherical Bessel functions, differentiation formulas      439
Spherical Bessel functions, duplication formula      440
Spherical Bessel functions, Gegenbauer’s generalization for      438
Spherical Bessel functions, generating functions for      439
Spherical Bessel functions, graphs of      438
Spherical Bessel functions, infinite series involving       440
Spherical Bessel functions, limiting values as $z\to 0$       437
Spherical Bessel functions, modulus and phase      439
Spherical Bessel functions, Poisson’s integral for      438
Spherical Bessel functions, Rayleigh’s formula for      439
Spherical Bessel functions, recurrence relations      439
Spherical Bessel functions, relation to Fresnel integrals      440
Spherical Bessel functions, representations by elementary functions      437
Spherical Bessel functions, tables of      457
Spherical Bessel functions, Wronskian relations      437
Spherical Bessel functions, zeros and their asymptotic expansions      440
Spherical polynomials (Legendre)      332; see “Orthogonal polynomials”
Spherical triangles, solution of      79
Spheroidal wave functions      751
Spheroidal wave functions, asymptotic behavior of      756
Spheroidal wave functions, asymptotic expansions of      755
Spheroidal wave functions, characteristic values for      753 756
Spheroidal wave functions, differential equations      753
Spheroidal wave functions, evaluation of coefficients for      755
Spheroidal wave functions, expansions for      755
Spheroidal wave functions, joining factors for      757
Spheroidal wave functions, normalization of      755
Spheroidal wave functions, table of eigenvalues of      760
Spheroidal wave functions, table of prolate joining factors      769
Spheroidal wave functions, tables of      766
Stirling numbers      824
Stirling numbers, table of the first kind      833
Stirling numbers, table of the second kind      835
Stirling’s formula      257
Struve’s functions      495
Struve’s functions, asymptotic expansions for large orders      498
Struve’s functions, asymptotic expansions for large |z|      497 498
Struve’s functions, computation of      499
Struve’s functions, differential equation      496
Struve’s functions, graphs of      496
Struve’s functions, integral representations of      496 498
Struve’s functions, integrals      497 498
Struve’s functions, modified      498
Struve’s functions, power series expansion for      496 498
Struve’s functions, recurrence relations      496 498
Struve’s functions, relation to Weber’s function      498
Struve’s functions, special properties of      497
Struve’s functions, tables of      501
Student’s t-distribution      948
Student’s t-distribution, approximations to      949
Student’s t-distribution, asymptotic expansion of      949
Student’s t-distribution, limiting distribution      949
Student’s t-distribution, non-central      949
Student’s t-distribution, series expansions for      948
Student’s t-distribution, statistical properties of      948
Subtabulation      881
Summable series      1005
Summation of rational series      264
Sums of positive powers      813
Sums of powers      804
Sums of reciprocal powers      807 811
Systems of differential equations of first order      897
Taylor expansion      880
Taylor’s Formula      14

Tesseral harmonics      332
Tetrachoric functions      934
Tetragamma function      260; see “Polygamma functions”
Theta functions      576
Theta functions, addition of quarter-periods      577
Theta functions, calculation by use of the arithmetic-geometric mean      577 580
Theta functions, expansions in terms of the nome q      576
Theta functions, Jacobi’s notation for      577
Theta functions, logarithmic derivatives of      576
Theta functions, logarithms of sum and difference      577
Theta functions, Neville’s notation for      578 582
Theta functions, relation to Jacobi’s zeta function      578
Theta functions, relation with Weierstrass elliptic functions      650
Theta functions, relations between squares of the functions      576
Thiele’s interpolation formula      881
Toroidal functions      336
Toronto function      509
Trapezoidal rule      885
Triangle inequality      11
Trigamma function      260; see “Polygamma functions”
Trigonometric functions      71; see “Circular functions’
Truncated exponential function      70 262
Ultraspherioal polynomials      774; see “Orthogonal polynomials”
Ultraspherioal polynomials, coefficients for and in terms of      794
Ultraspherioal polynomials, graphs of      776
Unit step function      1020
Variance      928
Variance-ratio distribution function      946; see “F-distribution function”
Vector-addition coefficients      1006
Wallis’ formula      258
Wave equation in prolate and oblate spheroidal coordinates      752
Weber’s function      498
Weber’s function, relation to Anger’s function      498
Weber’s function, relation to Struve’s function      498
Weierstrass elliptic functions      627
Weierstrass elliptic functions, addition formulas for      635
Weierstrass elliptic functions, case $\Delta=0$       651
Weierstrass elliptic functions, computation of      663
Weierstrass elliptic functions, conformal mapping of      642 654 659
Weierstrass elliptic functions, definitions      629
Weierstrass elliptic functions, derivatives of      640
Weierstrass elliptic functions, determination of periods from given invariants      665
Weierstrass elliptic functions, determination of values at half-periods, etc., from given periods      664
Weierstrass elliptic functions, differential equation      629 640
Weierstrass elliptic functions, discriminant      629
Weierstrass elliptic functions, equianharmonic case      652
Weierstrass elliptic functions, expressing any elliptic function in terms of $\mathscr P$ and $\mathscr P’$       651
Weierstrass elliptic functions, fundamental period parallelogram      629
Weierstrass elliptic functions, fundamental rectangle      630
Weierstrass elliptic functions, homogeneity relations      631
Weierstrass elliptic functions, integrals      641
Weierstrass elliptic functions, invariants      629
Weierstrass elliptic functions, Legendre’s relation      634
Weierstrass elliptic functions, lemniscatic case      658
Weierstrass elliptic functions, maps of      642 654 659
Weierstrass elliptic functions, multiplication formulas      635
Weierstrass elliptic functions, other series involving $\mathscr P, \mathscr P’, \zeta$       639
Weierstrass elliptic functions, pseudo-lemniscatic case      662
Weierstrass elliptic functions, reduction formulas      631
Weierstrass elliptic functions, relation with complete elliptic integrals      649
Weierstrass elliptic functions, relations with Jacobi's elliptic functions      649
Weierstrass elliptic functions, relations with theta functions      650
Weierstrass elliptic functions, reversed series for large $|\mathscr P|, |\mathscr P’|, |\zeta|$       638
Weierstrass elliptic functions, reversed series for small $|\sigma|$       640
Weierstrass elliptic functions, series expansions for      635
Weierstrass elliptic functions, special values and relations      633
Weierstrass elliptic functions, symbolism      629
Weierstrass elliptic functions, tables of      673
Whittaker functions      505
Wigner coefficients      1006
Zeta function Jacobi’s      578
Zeta function Riemann’s      256 807

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