Luke, Yudell L. The special functions and their approximations. Vol. I, II. (English) Zbl 0193.01701 Mathematics in Science and Engineering. 53. New York-London: Academic Press, I: xx, 349 pp. 19.50; II: xx, 485 pp. $ 24.50 (1969). Reviewer: S. K. Chatterjea Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 5 ReviewsCited in 894 Documents MSC: 33-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to special functions 33-02 Research exposition (monographs, survey articles) pertaining to special functions 33Cxx Hypergeometric functions Keywords:special functions × Cite Format Result Cite Review PDF Digital Library of Mathematical Functions: §10.23(iv) Compendia ‣ §10.23 Sums ‣ Bessel and Hankel Functions ‣ Chapter 10 Bessel Functions §10.60(iii) Other Series ‣ §10.60 Sums ‣ Spherical Bessel Functions ‣ Chapter 10 Bessel Functions §11.10(viii) Expansions in Series of Products of Bessel Functions ‣ §11.10 Anger–Weber Functions ‣ Related Functions ‣ Chapter 11 Struve and Related Functions §11.4(iv) Expansions in Series of Bessel Functions ‣ §11.4 Basic Properties ‣ Struve and Modified Struve Functions ‣ Chapter 11 Struve and Related Functions §11.9(ii) Expansions in Series of Bessel Functions ‣ §11.9 Lommel Functions ‣ Related Functions ‣ Chapter 11 Struve and Related Functions Chapter 11 Struve and Related Functions §12.20 Approximations ‣ Computation ‣ Chapter 12 Parabolic Cylinder Functions §13.31(i) Chebyshev-Series Expansions ‣ §13.31 Approximations ‣ Computation ‣ Chapter 13 Confluent Hypergeometric Functions §15.10(ii) Kummer’s 24 Solutions and Connection Formulas ‣ §15.10 Hypergeometric Differential Equation ‣ Properties ‣ Chapter 15 Hypergeometric Function §15.12(iii) Other Large Parameters ‣ §15.12 Asymptotic Approximations ‣ Properties ‣ Chapter 15 Hypergeometric Function §15.12(ii) Large 𝑐 ‣ §15.12 Asymptotic Approximations ‣ Properties ‣ Chapter 15 Hypergeometric Function Chapter 15 Hypergeometric Function §16.10 Expansions in Series of {_𝑝}𝐹_𝑞 Functions ‣ Generalized Hypergeometric Functions ‣ Chapter 16 Generalized Hypergeometric Functions and Meijer 𝐺-Function §16.11(iii) Expansions for Large Parameters ‣ §16.11 Asymptotic Expansions ‣ Generalized Hypergeometric Functions ‣ Chapter 16 Generalized Hypergeometric Functions and Meijer 𝐺-Function §16.11(iii) Expansions for Large Parameters ‣ §16.11 Asymptotic Expansions ‣ Generalized Hypergeometric Functions ‣ Chapter 16 Generalized Hypergeometric Functions and Meijer 𝐺-Function §16.17 Definition ‣ Meijer 𝐺-Function ‣ Chapter 16 Generalized Hypergeometric Functions and Meijer 𝐺-Function §16.18 Special Cases ‣ Meijer 𝐺-Function ‣ Chapter 16 Generalized Hypergeometric Functions and Meijer 𝐺-Function §16.18 Special Cases ‣ Meijer 𝐺-Function ‣ Chapter 16 Generalized Hypergeometric Functions and Meijer 𝐺-Function §16.19 Identities ‣ Meijer 𝐺-Function ‣ Chapter 16 Generalized Hypergeometric Functions and Meijer 𝐺-Function §16.20 Integrals and Series ‣ Meijer 𝐺-Function ‣ Chapter 16 Generalized Hypergeometric Functions and Meijer 𝐺-Function §16.21 Differential Equation ‣ Meijer 𝐺-Function ‣ Chapter 16 Generalized Hypergeometric Functions and Meijer 𝐺-Function §16.22 Asymptotic Expansions ‣ Meijer 𝐺-Function ‣ Chapter 16 Generalized Hypergeometric Functions and Meijer 𝐺-Function §16.5 Integral Representations and Integrals ‣ Generalized Hypergeometric Functions ‣ Chapter 16 Generalized Hypergeometric Functions and Meijer 𝐺-Function §16.5 Integral Representations and Integrals ‣ Generalized Hypergeometric Functions ‣ Chapter 16 Generalized Hypergeometric Functions and Meijer 𝐺-Function §16.5 Integral Representations and Integrals ‣ Generalized Hypergeometric Functions ‣ Chapter 16 Generalized Hypergeometric Functions and Meijer 𝐺-Function §16.7 Relations to Other Functions ‣ Generalized Hypergeometric Functions ‣ Chapter 16 Generalized Hypergeometric Functions and Meijer 𝐺-Function §16.8(iii) Confluence of Singularities ‣ §16.8 Differential Equations ‣ Generalized Hypergeometric Functions ‣ Chapter 16 Generalized Hypergeometric Functions and Meijer 𝐺-Function §16.8(ii) The Generalized Hypergeometric Differential Equation ‣ §16.8 Differential Equations ‣ Generalized Hypergeometric Functions ‣ Chapter 16 Generalized Hypergeometric Functions and Meijer 𝐺-Function Chapter 16 Generalized Hypergeometric Functions and Meijer 𝐺-Function In §25.20 Approximations ‣ Computation ‣ Chapter 25 Zeta and Related Functions Laplace Transform Inversion ‣ §3.11(iv) Padé Approximations ‣ §3.11 Approximation Techniques ‣ Areas ‣ Chapter 3 Numerical Methods §4.47(iv) Additional References ‣ §4.47 Approximations ‣ Computation ‣ Chapter 4 Elementary Functions §5.23(ii) Expansions in Chebyshev Series ‣ §5.23 Approximations ‣ Computation ‣ Chapter 5 Gamma Function §5.7(i) Maclaurin and Taylor Series ‣ §5.7 Series Expansions ‣ Properties ‣ Chapter 5 Gamma Function §6.10(ii) Expansions in Series of Spherical Bessel Functions ‣ §6.10 Other Series Expansions ‣ Properties ‣ Chapter 6 Exponential, Logarithmic, Sine, and Cosine Integrals In §6.20(ii) Expansions in Chebyshev Series ‣ §6.20 Approximations ‣ Computation ‣ Chapter 6 Exponential, Logarithmic, Sine, and Cosine Integrals In §6.20(ii) Expansions in Chebyshev Series ‣ §6.20 Approximations ‣ Computation ‣ Chapter 6 Exponential, Logarithmic, Sine, and Cosine Integrals In §6.20(ii) Expansions in Chebyshev Series ‣ §6.20 Approximations ‣ Computation ‣ Chapter 6 Exponential, Logarithmic, Sine, and Cosine Integrals In §6.20(iii) Padé-Type and Rational Expansions ‣ §6.20 Approximations ‣ Computation ‣ Chapter 6 Exponential, Logarithmic, Sine, and Cosine Integrals In §6.20(iii) Padé-Type and Rational Expansions ‣ §6.20 Approximations ‣ Computation ‣ Chapter 6 Exponential, Logarithmic, Sine, and Cosine Integrals §6.8 Inequalities ‣ Properties ‣ Chapter 6 Exponential, Logarithmic, Sine, and Cosine Integrals In §7.24(ii) Expansions in Chebyshev Series ‣ §7.24 Approximations ‣ Computation ‣ Chapter 7 Error Functions, Dawson’s and Fresnel Integrals In §7.24(iii) Padé-Type Expansions ‣ §7.24 Approximations ‣ Computation ‣ Chapter 7 Error Functions, Dawson’s and Fresnel Integrals §7.6(ii) Expansions in Series of Spherical Bessel Functions ‣ §7.6 Series Expansions ‣ Properties ‣ Chapter 7 Error Functions, Dawson’s and Fresnel Integrals §7.8 Inequalities ‣ Properties ‣ Chapter 7 Error Functions, Dawson’s and Fresnel Integrals §8.10 Inequalities ‣ Incomplete Gamma Functions ‣ Chapter 8 Incomplete Gamma and Related Functions Padé Approximants ‣ §8.10 Inequalities ‣ Incomplete Gamma Functions ‣ Chapter 8 Incomplete Gamma and Related Functions Spherical-Bessel-Function Expansions ‣ §8.21(vi) Series Expansions ‣ §8.21 Generalized Sine and Cosine Integrals ‣ Related Functions ‣ Chapter 8 Incomplete Gamma and Related Functions In §8.27(i) Incomplete Gamma Functions ‣ §8.27 Approximations ‣ Computation ‣ Chapter 8 Incomplete Gamma and Related Functions In §8.27(i) Incomplete Gamma Functions ‣ §8.27 Approximations ‣ Computation ‣ Chapter 8 Incomplete Gamma and Related Functions Chapter 8 Incomplete Gamma and Related Functions Online Encyclopedia of Integer Sequences: A series for Pi. Numerators of the coefficients of an asymptotic expansion in even powers of the Catalan numbers. Numerators of coefficients of an expansion of the logarithm of the Catalan numbers. Erroneous version of A006934.