##
**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).

### 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### 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

3rd item ‣ §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

3rd item ‣ §6.20(ii) Expansions in Chebyshev Series ‣ §6.20 Approximations ‣ Computation ‣ Chapter 6 Exponential, Logarithmic, Sine, and Cosine Integrals

4th item ‣ §6.20(ii) Expansions in Chebyshev Series ‣ §6.20 Approximations ‣ Computation ‣ Chapter 6 Exponential, Logarithmic, Sine, and Cosine Integrals

5th item ‣ §6.20(ii) Expansions in Chebyshev Series ‣ §6.20 Approximations ‣ Computation ‣ Chapter 6 Exponential, Logarithmic, Sine, and Cosine Integrals

1st item ‣ §6.20(iii) Padé-Type and Rational Expansions ‣ §6.20 Approximations ‣ Computation ‣ Chapter 6 Exponential, Logarithmic, Sine, and Cosine Integrals

2nd item ‣ §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

1st item ‣ §7.24(ii) Expansions in Chebyshev Series ‣ §7.24 Approximations ‣ Computation ‣ Chapter 7 Error Functions, Dawson’s and Fresnel Integrals

1st item ‣ §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

3rd item ‣ §8.27(i) Incomplete Gamma Functions ‣ §8.27 Approximations ‣ Computation ‣ Chapter 8 Incomplete Gamma and Related Functions

4th item ‣ §8.27(i) Incomplete Gamma Functions ‣ §8.27 Approximations ‣ Computation ‣ Chapter 8 Incomplete Gamma and Related Functions

Chapter 8 Incomplete Gamma and Related Functions