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| Luke Y.L. — Mathematical Functions and Their Approximations |
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| Предметный указатель |
Kummer's formulas 262 288
Laguerre polynomial (see also Expansion)
Laguerre polynomial, definition and basic properties 434 436
Laguerre polynomial, generalized and extended 232 238 239 447
Laplace transform and inverse Laplace transform of  and G-functions 161 162 188 189
Legendre and associated Legendre functions 280 283 299 433
Legendre polynomials 434 436
Logarithm 36 42 62 74 Expansion)
Logarithm, numerical values of particular numbers like ln 2 etc 512 514
Lommel functions 302 309 413 415
Mathematical constants 512 515
Mellin transforms of and G-functions 163 186
Mellin — Barnes integrals, evaluation of by trapezoidal integration rule 399
Minimal solution of difference equation 483
Named functions expressed as 's and G-functions 298 306 0
Orthogonal functions 428 431
Orthogonal polynomials 428 482 Chebyshev etc.)
Orthogonal polynomials, application to approximation and expansion of functions, see Approximation, Expansion classical, orthogonal properties of 434 436
Orthogonal polynomials, definition and basic properties 428 433
Pade approximation and table 493 495
Parabolic cylinder functions 296 297 300
Pi  , asymptotic expansion for 12
Pi , asymptotic expansion for value of 512 514
Polynomial approximation (see Approximation)
Polynomials (see Modifiers such as Bessel orthogonal etc.)
Power series, Pade approximation for 493
Powers of z , expansions for (see Expansion)
Psi  -function or logarithmic derivative of the gamma function (see also Approximation Expansion)
Psi -function or logarithmic derivative of the gamma function, definition and elementary properties 1 5 7 10
| Psi -function or logarithmic derivative of the gamma function, inequalities 19 20
Psi -function or logarithmic derivative of the gamma function, tables, references to 21
Racah coefficients 168
Rational approximation (see Approximation)
Recurrence formula (for) (see The listing below)
Recurrence formula (for) Bernoulli polynomials, generalized 507
Recurrence formula (for) Bessel functions 313
Recurrence formulas, use of in computation 98 102 219 220 380 395 464 468 475 482 483 489 511
Saalschuetz’s formula 163 164
Selected points, method of 498
Sine and cosine 52 61 Expansion)
Sine and cosine integrals 115 148 Expansion)
Special functions, references to 154
Struve functions and integrals 188 302 303 309 413 415 426 Expansion)
Tables (of), Bernoulli polynomials and numbers 505 506
Tables (of), coefficients for expansion of functions in series of Chebyshev polynomials of the first kind and for approximations in the form of polynomials and rational functions (see Approximation Expansion)
Tables (of), mathematical constants 512 515
Tangent and cotangent 53 61
Trapezoidal-type integration formulas 134 137 395 399
U-function (see Hypergeometric function (confluent))
Ultraspherical polynomial 434 436
Vandermonde’s theorem 272
Voigt function 121
Watson’s equation 164
Weber function (see Anger-Weber)
Whipplefs equation 164
Whittaker functions 295 (see also Hypergeometric function (confluent))
Wronskians 270 291 314
Y-transform 187
Zeta-function (Riemann) 22 510
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