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Abramowitz M., Stegun I. — Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables |
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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 -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 -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 358 379 381 385
Bessel functions graphs of 359 373
Bessel functions in terms of hypergeometric functions 362
Bessel functions notation 358
Bessel functions zeros of 370
Bessel functions zeros of cross products of 374
Bessel functions zeros, complex 372
Bessel functions zeros, infinite products for 370
Bessel functions zeros, McMahon’s expansions for 371
Bessel functions zeros, tables of 371 409 414
Bessel functions zeros, uniform expansions of 371
Bessel functions , addition theorems for 363
Bessel functions , analytic continuation of 361
Bessel functions , ascending series for 360
Bessel functions , asymptotic expansion for large arguments 364
Bessel functions , asymptotic expansions for large orders 365
Bessel functions , asymptotic expansions for zeros 371
Bessel functions , asymptotic expansions in the transition region for large orders 367
Bessel functions , asymptotic expansions of modulus and phase for large arguments 365
Bessel functions , connection with Legendre functions 362
Bessel functions , continued fractions for 363
Bessel functions , derivatives with respect to order 362
Bessel functions , differential equation 358
Bessel functions , differential equations for products 362
Bessel functions , formulas for derivatives 361
Bessel functions , generating function and associated series 361
Bessel functions , integral representations of 360
Bessel functions , limiting forms for small arguments 360
Bessel functions , modulus and phase 365
Bessel functions , multiplication theorem for 363
Bessel functions , Neumann’s expansion of an arbitrary function 363
Bessel functions , other differential equations 362
Bessel functions , polynomial approximations 369
Bessel functions , recurrence relations 361
Bessel functions , recurrence relations for cross-products 361
Bessel functions , relations between 358
Bessel functions , tables of 390
Bessel functions , uniform asymptotic expansions for large orders 358
Bessel functions , upper bounds 362
Bessel functions , 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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