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| Abramowitz M., Stegun I. (eds.) — Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Table |
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| Предметный указатель |
Hypergeometric functions, special elementary cases 556
Hypergeometric functions, special values of the argument 556
Hypergeometric functions, transformation formulas 559
Incomplete beta function 263 944
Incomplete beta function, approximations to 945
Incomplete beta function, asymptotic expansions of 945
Incomplete beta function, computation of 959
Incomplete beta function, continued fraction for 944
Incomplete beta function, recurrence formulas 263 944
Incomplete beta function, relation to other functions 945
Incomplete beta function, relation to the  -distribution 944
Incomplete beta function, relation to the binomial expansion 263
Incomplete beta function, relation to the hypergeometric function 263
Incomplete beta function, series expansion for 944
Incomplete beta function, symmetry relation 263
Incomplete gamma function 230 260 486 509
Incomplete gamma function as a confluent hypergeometric function 262
Incomplete gamma function, asymptotic expansions of 263
Incomplete gamma function, computation of 959
Incomplete gamma function, continued fraction for 263
Incomplete gamma function, definite integrals 263
Incomplete gamma function, derivatives and differential equations 262
Incomplete gamma function, graph of 261
Incomplete gamma function, Pearson's form of 262
Incomplete gamma function, recurrence formulas 262
Incomplete gamma function, series developments for 262
Incomplete gamma function, special values of 262
Incomplete gamma function, table of 978
Indeterminate forms (L'Hospital's rule) 13
Inequality, Cauchy's 11
Inequality, Chebyshev's 11
Inequality, Hoelder's for integrals 11
Inequality, Hoelder's for sums 11
Inequality, Minkowski's for integrals 11
Inequality, Minkowski's for sums 11
Inequality, Schwarz's 11
Inequality, triangle 11
Integral of a bivariate normal distribution over a polygon 956
Integrals of circular functions 77
Integrals of exponential functions 71
Integrals of hyperbolic functions 86
Integrals of inverse circular functions 82
Integrals of inverse hyperbolic functions 88
Integrals of irrational algebraic functions 12
Integrals of logarithmic functions 69
Integrals of rational algebraic functions 12
Integration 885
Integration by parts 12
Integration, Bode'srule 886
Integration, Chebyshev's equal weight formula 887
Integration, Euler — Maclaurin summation formula 886
Integration, Filon's formula 890
Integration, five-point rule for analytic functions 887
Integration, Gaussian type formulas 887
Integration, iterated integrals 891
Integration, Lagrange formula 886
Integration, Lobatto's integration formula 888
Integration, multidimensional 891
Integration, Newton — Cotes formula 886
Integration, Radau's integration formula 888
Integration, Simpson's rule 886
Integration, trapezoidal rule 885
Interpolation 878
Interpolation, Aitken's iteration method 879
Interpolation, Bessel's formula 881
Interpolation, bivariate 882
Interpolation, Everett's formula 880
Interpolation, harmonic analysis 881
Interpolation, inverse 881
Interpolation, Lagrange formula 878
Interpolation, Newton's divided difference formula 880
Interpolation, Newton's forward difference formula 880
Interpolation, Taylor's expansion 880
Interpolation, Thiele's formula 881
Interpolation, throwback formulas 880
Interpolation, trigonometric 881
Invariants 629
Invariants, tables of 680
Inverse circular functions 22 79 92
Inverse circular functions, addition and subtraction of 80
Inverse circular functions, Chebyshev approximations 82
Inverse circular functions, continued fractions for 81
Inverse circular functions, differentiation formulas 82
Inverse circular functions, graph of 79
Inverse circular functions, indefinite integrals 82
Inverse circular functions, logarithmic representation 80
Inverse circular functions, negative arguments 80
Inverse circular functions, polynomial approximations 81
Inverse circular functions, real and imaginary parts 80
Inverse circular functions, relation to inverse hyperbolic functions 80
Inverse circular functions, series expansions for 81
Inverse circular functions, table of 203
Inverse hyperbolic functions 86 93
Inverse hyperbolic functions, addition and subtraction of 87
Inverse hyperbolic functions, continued fractions for 88
Inverse hyperbolic functions, differentiation formulas 88
Inverse hyperbolic functions, graphs of 86
Inverse hyperbolic functions, indefinite integrals 88
Inverse hyperbolic functions, logarithmic representations 87
Inverse hyperbolic functions, negative arguments 87
Inverse hyperbolic functions, relation to inverse circular functions 87
Inverse hyperbolic functions, series expansions for 88
Inverse hyperbolic functions, tables of 221
Jacobi's eta function 577
Jacobi's polynomials 561 773 see
Jacobi's polynomials, coefficients for 793
Jacobi's polynomials, graphs of 773 776
Jacobi's theta function 576 see
Jacobi's zeta function 578 595
Jacobi's zeta function, addition theorem for 595
Jacobi's zeta function, calculation by use of the arithmetic-geometric mean 578
Jacobi's zeta function, graph of 595
Jacobi's zeta function, Jacobi's imaginary transformation 595
Jacobi's zeta function, q-series for 595
Jacobi's zeta function, relation to theta functions 578 595
Jacobi's zeta function, special values 595
Jacobi's zeta function, table of 619
Jacobian elliptic functions 567
Jacobian elliptic functions, addition theorems for 574
Jacobian elliptic functions, approximations in terms of circular functions 573
Jacobian elliptic functions, approximations in terms of hyperbolic functions 574
Jacobian elliptic functions, calculation by use of the arithmetic-geometric mean 571
Jacobian elliptic functions, calculation of 579 581
Jacobian elliptic functions, change of argument 572
Jacobian elliptic functions, change of parameter 573
Jacobian elliptic functions, classification of 570
Jacobian elliptic functions, complex arguments 575
Jacobian elliptic functions, definitions 569
Jacobian elliptic functions, derivatives of 574
Jacobian elliptic functions, double arguments 574
Jacobian elliptic functions, graphs of 570
Jacobian elliptic functions, half-arguments 574
Jacobian elliptic functions, integrals 575
Jacobian elliptic functions, integrals of the squares 576
Jacobian elliptic functions, Jacobi's imaginary transformation 574
Jacobian elliptic functions, Landen transformation 573
Jacobian elliptic functions, leading terms of series in powers of u 575
Jacobian elliptic functions, parameter 569
Jacobian elliptic functions, principal terms 572
Jacobian elliptic functions, quarter periods 569
Jacobian elliptic functions, reciprocal parameter 573
Jacobian elliptic functions, relation to the copolar trio 570
Jacobian elliptic functions, relation with Weierstrass functions 649
Jacobian elliptic functions, relations between squares of the functions 573
Jacobian elliptic functions, series expansions in terms of the nome q 575
Jacobian elliptic functions, special arguments 571
Kelvin functions 379 387 509
Kelvin functions of negative argument 380
Kelvin functions, ascending series for 379
Kelvin functions, ascending series for products of 381
| Kelvin functions, asymptotic expansions for large arguments 381
Kelvin functions, asymptotic expansions for large zeros 383
Kelvin functions, asymptotic expansions of modulus and phase 383
Kelvin functions, asymptotic expansions of products 383
Kelvin functions, definitions 379
Kelvin functions, differential equations 379
Kelvin functions, expansions in series of Bessel functions 381
Kelvin functions, graphs of 382
Kelvin functions, indefinite integrals 380
Kelvin functions, modulus and phase 382
Kelvin functions, polynomial approximations 384
Kelvin functions, recurrence relations 380
Kelvin functions, recurrence relations for products 380
Kelvin functions, relations between 379
Kelvin functions, tables of 430
Kelvin functions, uniform asymptotic expansions for large orders 384
Kelvin functions, zeros of functions of order zero 381
Kronecker delta 822
Kummer functions 504
Kummer's transformation of series 16
l'Hospital's rule 13
Lagrange differentiation formula 882
Lagrange integration coefficients 886
Lagrange integration coefficients, table of 915
Lagrange interpolation coefficients 878
Lagrange interpolation coefficients, table of 900
Lagrange interpolation formula 878
Lagrange's expansion 14
Laguerre integration 890
Laguerre integration, abscissas and weight factors for 923
Laguerre polynomials 509 510 773 see
Laguerre polynomials, coefficients for and  in terms of 799
Laguerre polynomials, graph of 780
Laguerre polynomials, values of 800
Lame's equation 641
Landen's transformation, ascending 573 598 604
Landen's transformation, descending 573 597 604
Laplace transforms 1019
Laplace transforms, definition 1020
Laplace transforms, operations 1020
Laplace transforms, tables of 1021
Laplace — Stieltjes transforms 1029
Laplace — Stieltjes transforms, tables of 1029
Laplace's equation 17
Laplacian 885
Laplacian in spherical coordinates 752
Laurent series 635
Least square approximations 790
Legendre functions 332 362 377 561 774
Legendre functions of negative argument 333
Legendre functions of negative degree 333
Legendre functions of negative order 333
Legendre functions, asymptotic expansions of 335
Legendre functions, computation of 339
Legendre functions, explicit expressions for 333
Legendre functions, graphs of 338 780
Legendre functions, integral representations of 335
Legendre functions, integrals involving 337
Legendre functions, notation for 332
Legendre functions, recurrence relations 333
Legendre functions, relation to elliptic integrals 337
Legendre functions, relations between 333
Legendre functions, Rodrigues' formula 334
Legendre functions, special values of 334
Legendre functions, summation formulas 335
Legendre functions, tables of 342
Legendre functions, trigonometric expansions of 335
Legendre functions, values on the cut 333
Legendre functions, Wronskian relation 333
Legendre polynomials 332 486 773 see
Legendre polynomials, coefficients for and in terms of 798
Legendre polynomials, graph of 338 780
Legendre polynomials, values of 342
Legendre's differential equation 332
Legendre's differential equation, solutions of 332
Leibniz' theorem for differentiation of a product 12
Leibniz' theorem for differentiation of an integral 11
Lemniscate constant 658
Lemniscatic case 658
Lobatto integration 888
Lobatto integration, abscissas and weight factors for 920
Logarithmic function 67 89
Logarithmic function, change of base 67 89
Logarithmic function, characteristic 89
Logarithmic function, Chebyshev approximations 69
Logarithmic function, common 68 89
Logarithmic function, continued fractions for 68
Logarithmic function, definite integrals 69
Logarithmic function, differentiation formula 69
Logarithmic function, graph of 67
Logarithmic function, indefinite integrals 69
Logarithmic function, inequalities for 68
Logarithmic function, limiting values 68
Logarithmic function, mantissa 89
Logarithmic function, polynomial approximations 68
Logarithmic function, series expansions for 68
Logarithmic function, tables of 95
Logarithmic integral 228 231 510
Logarithmic integral, graph of 231
Markoff's differentiation formula 883
Mathematical constants 1
Mathematical constants in octal scale 1017
Mathieu functions 721
Mathieu functions, asymptotic representations of 740
Mathieu functions, comparative notation for 744
Mathieu functions, expansions for small q 730
Mathieu functions, expansions in terms of parabolic cylinder functions 742
Mathieu functions, graphs of 725 734
Mathieu functions, integral equations for 735
Mathieu functions, integral representations of 736
Mathieu functions, joining factors, table of 748
Mathieu functions, normalization of 732
Mathieu functions, orthogonality properties of 732
Mathieu functions, other properties of 735 738
Mathieu functions, power series in q for periodic solutions 725
Mathieu functions, proportionality factors 735
Mathieu functions, recurrence relations among the coefficients 723
Mathieu functions, special cases of 728
Mathieu functions, special values of 740
Mathieu functions, table of coefficients for 750
Mathieu functions, table of critical values of 748
Mathieu functions, zeros of 739
Mathieu's equation 722
Mathieu's equation, characteristic exponent 727
Mathieu's equation, characteristic exponent, generation of 727
Mathieu's equation, characteristic exponent, graphs of 728
Mathieu's equation, characteristic values 722 748
Mathieu's equation, characteristic values, asymptotic expansions of 726
Mathieu's equation, characteristic values, determination of 722
Mathieu's equation, characteristic values, graph of 724
Mathieu's equation, characteristic values, power series for 724
Mathieu's equation, Floquet solutions 727
Mathieu's equation, other solutions 730
Mathieu's equation, relation to spheroidal wave equation 722
Mathieu's equation, solutions involving products of Bessel functions 731
Mathieu's equation, stability regions of 728
Mathieu's modified equation 722
Mathieu's modified equation, radial solutions of 732
Maxima 14
Mean 928
Mean, arithmetic 10
Mean, generalized 10
Mean, geometric 10
Mean, harmonic 10
Milne's method 896
Minima 14
Minkowski's inequality for integrals 11
Minkowski's inequality for sums 11
Miscellaneous functions 997
Modified Bessel functions  374
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