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

Modified Bessel functions in terms of hypergeometric functions      377
Modified Bessel functions, $I_{\nu}(z), K_{\nu}(z)$       374
Modified Bessel functions, analytic continuation of      376
Modified Bessel functions, ascending series for      375
Modified Bessel functions, asymptotic expansions for large arguments      377
Modified Bessel functions, connection with Legendre functions      377
Modified Bessel functions, derivatives with respect to order      377
Modified Bessel functions, differential equation      374
Modified Bessel functions, formulas for derivatives      376
Modified Bessel functions, generating function and associated series      376
Modified Bessel functions, graphs of      374
Modified Bessel functions, integral representations of      376
Modified Bessel functions, limiting forms for small arguments      375
Modified Bessel functions, multiplication theorems for      377
Modified Bessel functions, Neumann series for $K_{\nu}(z)$       377
Modified Bessel functions, other differential equations      377
Modified Bessel functions, polynomial approximations      378
Modified Bessel functions, recurrence relations      376
Modified Bessel functions, relations between      375
Modified Bessel functions, tables of      416
Modified Bessel functions, uniform asymptotic expansions for large orders      378
Modified Bessel functions, Wronskian relations      375
Modified Bessel functions, zeros of      377
Modified Mathieu functions      722
Modified Mathieu functions, graphs of      734
Modified spherical Bessel functions      443 453 498
Modified spherical Bessel functions, addition theorems for      445
Modified spherical Bessel functions, ascending series for      443
Modified spherical Bessel functions, computation of      453
Modified spherical Bessel functions, definitions      443
Modified spherical Bessel functions, degenerate forms      445
Modified spherical Bessel functions, derivatives with respect to order      445
Modified spherical Bessel functions, differential equation      443
Modified spherical Bessel functions, differentiation formulas      444
Modified spherical Bessel functions, duplication formula      445
Modified spherical Bessel functions, formulas of Rayleigh’s type      445
Modified spherical Bessel functions, generating functions for      445
Modified spherical Bessel functions, graphs of      444
Modified spherical Bessel functions, recurrence relations      444
Modified spherical Bessel functions, representations by elementary functions      443
Modified spherical Bessel functions, tables of      469
Modified spherical Bessel functions, Wronskian relations      443
Modified Struve functions      498
Modified Struve functions, asymptotic expansion for large |z|      498
Modified Struve functions, computation of      499
Modified Struve functions, graph of      498
Modified Struve functions, integral representations of      498
Modified Struve functions, integrals      498
Modified Struve functions, power series expansion for      498
Modified Struve functions, recurrence relations      498
Modified Struve functions, relation to modified spherical Bessel functions      498
Modified Struve functions, tables of      501
Modulus      16
Moments      928
Multidimensional integration      891
Multinomial coefficients      823
Multinomial coefficients, table of      831
Neumann’s polynomial      363
Neville’s notation      578
Neville’s theta functions      578
Neville’s theta functions, expression as infinite products      579
Neville’s theta functions, expression as infinite series      579
Neville’s theta functions, graphs of      578
Neville’s theta functions, tables of      582
Newton coefficients      880
Newton coefficients, relation to Lagrange coefficients      880
Newton interpolation formula      880 883
Newton — Cotes formula      886
Newton’s method of approximation      18
Nome      591 602
Nome, table of      608 610 612
Normal probability density function derivatives of      933
Normal probability function      931
Normal probability function asymptotic expansions of      932
Normal probability function bounds for      933
Normal probability function computation of      953
Normal probability function continued fraction for      932
Normal probability function error curves for      933
Normal probability function power series for      932
Normal probability function relation to other functions      934
Normal probability function values of x for extreme values of P(x) and Q(z)      977
Normal probability function values of x in terms of P(x) and Q(x)      976
Normal probability function values of Z(x) in terms of P(x) and Q(x)      975
Normal probability function, polynomial and rational approximations      932
Normal probability functions and derivatives      933
Normal probability functions and derivatives tables of      966
Normal probability integral repeated integrals of      934
Number theoretic functions      826
Oblate spheroidal coordinates      752
Octal scale      1017
Octal tables      1017
Operations with series      15
Orthogonal polynomials      771
Orthogonal polynomials as confluent hypergeometric functions      780
Orthogonal polynomials as hypergeometric functions      779
Orthogonal polynomials as Legendre functions      780
Orthogonal polynomials as parabolic cylinder functions      780
Orthogonal polynomials coefficients for      793
Orthogonal polynomials definition      773
Orthogonal polynomials differential equations      773 781
Orthogonal polynomials differential relations      783
Orthogonal polynomials evaluation of      788
Orthogonal polynomials explicit expressions for      775
Orthogonal polynomials generating functions for      783
Orthogonal polynomials graphs of      773 776—780
Orthogonal polynomials inequalities for      786
Orthogonal polynomials integral representations of      784
Orthogonal polynomials integrals involving      785
Orthogonal polynomials interrelations      777
Orthogonal polynomials limit relations      787
Orthogonal polynomials of a discrete variable      788
Orthogonal polynomials, change of interval of orthogonality      790
Orthogonal polynomials, orthogonality relations      774
Orthogonal polynomials, powers of x in terms of      793 794—801
Orthogonal polynomials, recurrence relations with respect to degree n      782
Orthogonal polynomials, recurrence relations, miscellaneous      773 782
Orthogonal polynomials, Rodrigues’ formula      773 785
Orthogonal polynomials, special values of      777
Orthogonal polynomials, sum formulas      785
Orthogonal polynomials, tables of      795 796 800 802
Orthogonal polynomials, zeros of      787
Parabolic cylinder functions U(a,x), V(a,x)      300 509 685 780
Parabolic cylinder functions U(a,x), V(a,x), asymptotic expansions of      689
Parabolic cylinder functions U(a,x), V(a,x), computation of      697
Parabolic cylinder functions U(a,x), V(a,x), connection with Bessel functions      692 697
Parabolic cylinder functions U(a,x), V(a,x), connection with confluent hypergeometric functions      691
Parabolic cylinder functions U(a,x), V(a,x), connection with Hermite polynomials and functions      691
Parabolic cylinder functions U(a,x), V(a,x), connection with probability integrals and Dawson’s integral      691
Parabolic cylinder functions U(a,x), V(a,x), Darwin’s expansions      689
Parabolic cylinder functions U(a,x), V(a,x), differential equation      686
Parabolic cylinder functions U(a,x), V(a,x), expansions for a large, x moderate      689
Parabolic cylinder functions U(a,x), V(a,x), expansions fora large, o moderate      689
Parabolic cylinder functions U(a,x), V(a,x), expansions in terms of Airy functions      689
Parabolic cylinder functions U(a,x), V(a,x), integral representations of      687
Parabolic cylinder functions U(a,x), V(a,x), modulus and phase      690
Parabolic cylinder functions U(a,x), V(a,x), power series in x for      686
Parabolic cylinder functions U(a,x), V(a,x), recurrence relations      688
Parabolic cylinder functions U(a,x), V(a,x), standard solutions      687
Parabolic cylinder functions U(a,x), V(a,x), table of      700
Parabolic cylinder functions U(a,x), V(a,x), Wronskian and other relations      687
Parabolic cylinder functions U(a,x), V(a,x), zeros of      696
Parabolic cylinder functions W(a, x)      692
Parabolic cylinder functions W(a, x), asymptotic expansions of      693
Parabolic cylinder functions W(a, x), complex solutions      693
Parabolic cylinder functions W(a, x), computation of      699
Parabolic cylinder functions W(a, x), connection with Bessel functions      695
Parabolic cylinder functions W(a, x), connection with confluent hypergeometric functions      695
Parabolic cylinder functions W(a, x), Darwin’s expansions      694
Parabolic cylinder functions W(a, x), differential equation      686 692
Parabolic cylinder functions W(a, x), expansions for a large, x moderate      694

Parabolic cylinder functions W(a, x), expansions for x large, a moderate      693
Parabolic cylinder functions W(a, x), expression in terms of Airy functions      693
Parabolic cylinder functions W(a, x), integral representations of      693
Parabolic cylinder functions W(a, x), modulus and phase      695
Parabolic cylinder functions W(a, x), power series in x for      692
Parabolic cylinder functions W(a, x), standard solutions      692
Parabolic cylinder functions W(a, x), table of      712
Parabolic cylinder functions W(a, x), Wronskian and other relations      693
Parabolic cylinder functions W(a, x), zeros of      696
Parameter m      569 602
Parameter m, table of      612
Partitions      825
Partitions into distinct parts      825
Partitions tables of      831 836
Partitions unrestricted      825
Pearson’s form of the incomplete gamma function      262
Pentagamma function      260; see “Polygamma functions”
Percentage points of the $\chi^2$ -distribution values of $\chi^2$ in terms of Q and $\nu$       984
Percentage points of the F-distribution values of F in terms of $Q,\nu_1,\nu_2$       986
Percentage points of the t-distribution values of t in terms of A and $\nu$       990
Planck’s radiation function      999
Plane triangles, solution of      78 92
Pochhammer’s symbol      256
Point-slope formula      896
Poisson distribution      959
Poisson distribution, table of cumulative sums of      978
Poisson — Charlier function      509
Polar form      16
Polygamma functions      260
Polygamma functions fractional values of      260
Polygamma functions integer values of      260
Polygamma functions multiplication formula for      260
Polygamma functions series expansions for      260
Polygamma functions tables of      267 271
Polygamma functions, asymptotic formulas      260
Polygamma functions, recurrence formula      260
Polygamma functions, reflection formula      260
Polynomial evaluation      788
Powers $x^n/\eta!$       818
Powers $x^n/\eta!$ tables of      24
Powers computation of      19 90
Powers general      69
Powers graph of      19
Powers of complex numbers      16
Powers of two      1016
Predictor-corrector method      896
PRIMES      231
Primes table of      870
Primitive roots      827
Primitive roots table of      864
Probability density function      931
Probability density function asymptotic expansion of      935
Probability functions      927
Probability integral      262 691
Probability integral of the $\chi^2$ -distribution, table of      978
Progressions arithmetic      10
Progressions geometric      10
Prolate spheroidal coordinates      752
Pseudo-lemniscatic case      662
Psi function      258 264
Psi function in the complex plane      259
Psi function, asymptotic formulas      259
Psi function, definite integrals      259
Psi function, duplication formula      259
Psi function, fractional values of      258
Psi function, graph of      258
Psi function, integer values of      258
Psi function, recurrence formulas      258
Psi function, reflection formula      259
Psi function, series expansions for      259
Psi function, tables of      267 272 276 288
Psi function, zeros of      259
Quadratic equation, solution of      17 19
Quartic equation, resolution into quadratic factors      17 20
Radau’s integration formula      888
Random deviates, generation of      949
Random numbers      949
Random numbers, methods of generation of      949
Random numbers, table of      991
Repeated integrals of the error function      299
Repeated integrals of the error function, as a single integral      299
Repeated integrals of the error function, asymptotic expansion of      300
Repeated integrals of the error function, definition      299
Repeated integrals of the error function, derivatives of      300
Repeated integrals of the error function, differential equation      299
Repeated integrals of the error function, graph of      300
Repeated integrals of the error function, power series for      299
Repeated integrals of the error function, recurrence relations      299
Repeated integrals of the error function, relation to Hermite polynomials      300
Repeated integrals of the error function, relation to parabolic cylinder functions      300
Repeated integrals of the error function, relation to the confluent hypergeometric function      300
Repeated integrals of the error function, relation to the Hh function      300
Repeated integrals of the error function, table of      317
Repeated integrals of the error function, value at zero      300
Representation of numbers      1012
Reversion of series      16 882
Riccati — Bessel functions      445
Riccati — Bessel functions definitions      445
Riccati — Bessel functions, differential equation      445
Riccati — Bessel functions, Riemann zeta function      256 807
Riccati — Bessel functions, special values of      807
Riccati — Bessel functions, Wronskian relations      445
Riemann’s differential equation      564
Riemann’s differential equation, solutions of      564
Riemann’s P function      564
Riemann’s P function, transformation formulas      565
Ring functions      336
Rodrigues’ formula      334 773 785
Roots computation of      19 89
Roots graph of      19
Roots of complex numbers      17 20
Roots tables of      24 223
Runge — Kutta methods      896
Scales of notation      1011
Scales of notation, general conversion methods      1012
Schwarz’s inequality      11
Sectoral harmonics      332
Series      14
Series binomial      14
Series Euler — Maclaurin summation formula      16 22
Series Euler’s transformation of      16 21
Series exponential      69
Series Kummer’s transformation of      16
Series Lagrange’s expansion      14
Series logarithmic      68
Series operations with      15
Series reversion of      16
Series Taylor's      14
Series trigonometric      74
Shifted Chebyshev polynomials      774; see “Orthogonal polynomials”
Shifted Legendre polynomials      774; see “Orthogonal polynomials”
Sievert integral      1000
Simpson’s rule      886
Sine integral      231 510
Sine integral definitions      231
Sine integral, asymptotic expansions of      233
Sine integral, computation of      233
Sine integral, graphs of      232
Sine integral, integral representation of      232
Sine integral, integrals      232
Sine integral, rational approximations      233
Sine integral, relation to exponential integral      232
Sine integral, series expansions for      232
Sine integral, symmetry relations      232
Sine integral, tables of      238 243
skewness      928
Spence’s integral      1004
Spherical Bessel functions      230 301 435 540
Spherical Bessel functions, addition theorems for      440
Spherical Bessel functions, analytic continuation of      439

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