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| Abramowitz M., Stegun I.A. (eds.) — Handbook of mathematical functions (without numerical tables) |
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Название: Handbook of mathematical functions (without numerical tables)
Авторы: Abramowitz M., Stegun I.A. (eds.)
Язык: 
Рубрика: Математика/
Статус предметного указателя: Готов указатель с номерами страниц
ed2k:
Издание: 10
Год издания: 1972
Количество страниц: 512
Добавлена в каталог: 02.10.2015
Операции: Положить на полку |
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| Предметный указатель |
Differences, reciprocal 878
Differential equations 896
Differential equations of second order with turning points 450
Differential equations, ordinary first order 896
Differential equations, solution by Adam's formulas 896
Differential equations, solution by Adam's formulas by Gill's method 896
Differential equations, solution by Adam's formulas by Milne's method 896
Differential equations, solution by Adam's formulas by point-slope formula 896
Differential equations, solution by Adam's formulas by predictor-corrector methods 896
Differential equations, solution by Adam's formulas by Runge — Kutta method 896
Differential equations, solution by trapezoidal formula 896
Differential equations, system of 897
Differentiation 882
Differentiation coefficients 882
Differentiation coefficients, table of 914
Differentiation, Everett's formula 883
Differentiation, Lagrange's formula 882
Differentiation, Markoff's formula 883
Digamma function 258 see
Dilogarithm function 1004
Distribution functions 927
Distribution functions, asymptotic expansions of 935
Distribution functions, characteristics of 928
Distribution functions, continuous 927
Distribution functions, discrete 927
Distribution functions, inequalities for 931
Distribution functions, lattice 927
Distribution functions, one-dimensional continuous 930
Distribution functions, one-dimensional discrete 929
Divisor functions 827
Divisor functions, table of 840
Double precision operations 21
Economization of series 791
Edgeworth asymptotic expansion 935 955
Einstein functions 999
Elliptic integrals 587
Elliptic integrals of the first kind 589
Elliptic integrals of the second kind 589
Elliptic integrals of the third kind 590 599
Elliptic integrals, amplitude 590
Elliptic integrals, canonical forms 589
Elliptic integrals, characteristic 590
Elliptic integrals, complete 590
Elliptic integrals, complete of the first kind 590
Elliptic integrals, complete of the second kind 590
Elliptic integrals, complete of the third kind 599 605
Elliptic integrals, complete, computation of 601
Elliptic integrals, complete, infinite series for 591
Elliptic integrals, complete, Legendre's relation 591
Elliptic integrals, complete, limiting values 591
Elliptic integrals, complete, polynomial approximations 591
Elliptic integrals, complete, q-series for 591
Elliptic integrals, complete, relation to hypergeometric functions 591
Elliptic integrals, definition 589
Elliptic integrals, graphs of the complete 592
Elliptic integrals, graphs of the first kind 592 593
Elliptic integrals, graphs of the incomplete 593 594
Elliptic integrals, graphs of the second kind 592 594
Elliptic integrals, graphs of the third kind 600
Elliptic integrals, incomplete 592
Elliptic integrals, incomplete, amplitude near  593
Elliptic integrals, incomplete, amplitude of any magnitude 592
Elliptic integrals, incomplete, complex amplitude 592
Elliptic integrals, incomplete, computations involving 595 602 605
Elliptic integrals, incomplete, imaginary amplitude 594
Elliptic integrals, incomplete, Jacobi's imaginary transformation 592
Elliptic integrals, incomplete, negative amplitude 592
Elliptic integrals, incomplete, negative parameter 593
Elliptic integrals, incomplete, numerical evaluation of 595
Elliptic integrals, incomplete, parameter greater than unity 593
Elliptic integrals, incomplete, special cases of 594
Elliptic integrals, modular angle 590
Elliptic integrals, modulus 590
Elliptic integrals, parameter 590 602
Elliptic integrals, reduction formulas 589 597
Elliptic integrals, reduction to canonical form 600
Elliptic integrals, relation to Weierstrass elliptic functions 649
Elliptic integrals, tables of complete 608
Elliptic integrals, tables of the incomplete 613
Elliptic integrals, tables of the third kind 625
Elliptical coordinates 752
Equianharmonic case 652
Error function 262 297 301 304 306 509
Error function, altitude chart in the complex plane 298
Error function, asymptotic expansion of 298
Error function, complex zeros of 329
Error function, continued fraction for 298
Error function, definite and indefinite integrals related to 302
Error function, derivatives of 298
Error function, graphs of 297
Error function, inequalities for 298
Error function, infinite series approximation for the complex function 299
Error function, integral representation of 297
Error function, rational approximations 299
Error function, relation to the confluent hypergeometric function 298
Error function, repeated integrals of 299
Error function, series expansions for 297
Error function, symmetry relations 297
Error function, table for complex arguments 325
Error function, table of repeated integrals of 317
Error function, tables of 310 312 316
Error function, value at infinity 298
Error, absolute 14
Error, percentage 14
Error, relative 14
Eta functions 577
Euler function 826
Euler function, table of 840
Euler numbers 804
Euler numbers, table of 810
Euler polynomials 803
Euler polynomials as sums of powers 804
Euler polynomials, coefficients of 809
Euler polynomials, derivatives of 804
Euler polynomials, differences of 804
Euler polynomials, expansions of 804
Euler polynomials, Fourier expansions of 805
Euler polynomials, generating function for 804
Euler polynomials, inequalities for 805
Euler polynomials, integrals involving 805
Euler polynomials, multiplication theorem for 804
Euler polynomials, relations with Bernoulli polynomials 806
Euler polynomials, special values of 805
Euler polynomials, symbolic operations 806
Euler polynomials, symmetry relations 804
Euler summation formula 806
Euler — Maclaurin formulas 806
Euler — Maclaurin summation formula 16 22 806 886
Euler — Totient function 826
Euler's constant 255
Euler's formula 74 255
Euler's integral 255
Euler's transformation of series 16 21
Everett interpolation coefficients 880
Everett interpolation coefficients, relation to Lagrange coefficients 880
Everett's formula 880 883
Excess 928
Expected value operator 928
Exponential function 69 90 509
Exponential function, Chebyshev approximation 71
Exponential function, continued fractions for 70
Exponential function, differentiation formulas 71
Exponential function, Euler's formula 74
Exponential function, graph of 70
Exponential function, identities 70
Exponential function, indefinite integrals 71
Exponential function, inequalities for 70
Exponential function, limiting values 70
Exponential function, periodic property of 70
Exponential function, polynomial approximations 71
| Exponential function, series expansions for 69
Exponential function, tables of 116 140 219
Exponential integral 227 262 510
Exponential integral, asymptotic expansion of 231
Exponential integral, computation of 233
Exponential integral, continued fraction for 229
Exponential integral, definite integrals 230
Exponential integral, derivatives of 230
Exponential integral, graphs of 228
Exponential integral, indefinite integrals 230
Exponential integral, inequalities for 229
Exponential integral, interrelations 228
Exponential integral, polynomial approximations 231
Exponential integral, rational approximations 231
Exponential integral, recurrence relations 229
Exponential integral, relation to incomplete gamma function 230
Exponential integral, relation to spherical Bessel functions 230
Exponential integral, series expansions for 229
Exponential integral, tables of 238 243 245 248 249 251
F-distribution function 946
F-distribution function, approximations to 947 948
F-distribution function, computation of 961
F-distribution function, limiting forms 947 948
F-distribution function, non-central 947
F-distribution function, reflexive relation 946
F-distribution function, relation to Student's t-distribution 947
F-distribution function, relation to the  -distribution 946
F-distribution function, series expansions for 946 948
F-distribution function, statistical properties of 946
Factorial function 255 see
Factorization, table of 844 864
Faltung theorem 1020
Filon's quadrature formula 890
Filon's quadrature formula, coefficients for 924
Floquet's theorem 727
Fresnel integrals 262 300 440
Fresnel integrals, asymptotic expansions of 302
Fresnel integrals, auxiliary functions 300 323
Fresnel integrals, complex zeros of 329
Fresnel integrals, definition 300
Fresnel integrals, derivatives of 301
Fresnel integrals, graph of 301
Fresnel integrals, integrals involving 303
Fresnel integrals, interrelations 300
Fresnel integrals, maxima and minima of 329
Fresnel integrals, rational approximations 302
Fresnel integrals, relation to spherical Bessel functions 301
Fresnel integrals, relation to the confluent hypergeometric function 301
Fresnel integrals, relation to the error function 301
Fresnel integrals, series expansion for 301
Fresnel integrals, symmetry relations 301
Fresnel integrals, table of 321 323
Fresnel integrals, value at infinity 301
Fundamental period parallelogram 629
Gamma function 255 263
Gamma function in the complex plane 256
Gamma function, asymptotic formulas 257
Gamma function, binomial coefficient 256
Gamma function, continued fraction for 258
Gamma function, definite integrals 258
Gamma function, duplication formula 256
Gamma function, Euler's formula 255
Gamma function, Euler's infinite product 255
Gamma function, Euler's integral 255
Gamma function, fractional values of 255
Gamma function, Gauss' multiplication formula 256
Gamma function, graph of 255
Gamma function, Hankers contour integral 255
Gamma function, integer values of 255
Gamma function, Pochhammer's symbol 256
Gamma function, polynomial approximations 257
Gamma function, power series for 256
Gamma function, recurrence formulas 256
Gamma function, reflection formula 256
Gamma function, series expansion for l/r(z) 256
Gamma function, Stirling's formula 257
Gamma function, tables of 267 272 274 276
Gamma function, triplication formulas 256
Gamma function, Wallis' formula 258
Gauss series 556
Gauss' transformation 573
Gaussian integration 887
Gaussian integration for integrands with a logarithmic singularity 920
Gaussian integration of moments 921
Gaussian integration, abscissas and weight factors for 916
Gaussian probability function 931
Gegenbauer polynomials 561 see
Gegenbauer polynomials, coefficients for and  in terms of 794
Gegenbauer polynomials, graphs of 776
Generalized hypergeometric function 362 377 556
Generalized Laguerre polynomials 771 see
Generalized mean 10
Geometric mean 10
Geometric progression 10
Gill's method 896
Gudermannian 77
Hankel functions 358 379 510
Hankers contour integral 255
Harmonic analysis 202 881
Harmonic mean 10
Haversine 78
Heaviside expansion theorem 1021
Hermite functions 509 691
Hermite integration 890
Hermite integration, abscissas and weight factors for 924
Hermite polynomials 300 510 691 775 see
Hermite polynomials, coefficients for and in terms of 801
Hermite polynomials, graph of 780
Hermite polynomials, values of 802
Heuman's lambda function 595
Heuman's lambda function, graph of 595
Heuman's lambda function, table of 622
Hh function 300 691
Hoelder's inequality for integrals 11
Hoelder's inequality for integrals for sums 11
Horner's scheme 788
Hyperbolic functions 83
Hyperbolic functions, addition and subtraction of 84
Hyperbolic functions, addition formulas for 83
Hyperbolic functions, continued fraction for 85
Hyperbolic functions, DeMoivre's theorem 84
Hyperbolic functions, differentiation formulas 85
Hyperbolic functions, graph of 83
Hyperbolic functions, half-angle formulas 83
Hyperbolic functions, indefinite integrals 86
Hyperbolic functions, infinite products 85
Hyperbolic functions, modulus and phase 84
Hyperbolic functions, multiple angle formulas 84
Hyperbolic functions, negative angle formulas 83
Hyperbolic functions, periodic properties of 83
Hyperbolic functions, products of 84
Hyperbolic functions, real and imaginary parts 84
Hyperbolic functions, relation to circular functions 83
Hyperbolic functions, relations between 83
Hyperbolic functions, series expansions for 85
Hyperbolic functions, tables of 213 219
Hypergeometric differential equation 562
Hypergeometric differential equation, solution of 563
Hypergeometric functions 332 335 336 362 377 487 555 779
Hypergeometric functions as Legendre functions 561
Hypergeometric functions as polynomials 561
Hypergeometric functions as reductions of Riemann's P-function 565
Hypergeometric functions, asymptotic expansions of 565
Hypergeometric functions, differentiation formulas 1 557
Hypergeometric functions, Gauss series 556
Hypergeometric functions, Gauss' relations for contiguous functions 557
Hypergeometric functions, integral representations 558
Hypergeometric functions, special cases of 561
Hypergeometric functions, special elementary cases 556
Hypergeometric functions, special values of the argument 556
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