Chapter 16 Generalized Hypergeometric Functions and Meijer $G$-Function

R. A. Askey Department of Mathematics, University of Wisconsin, Madison, Wisconsin. A. B. Olde Daalhuis School of Mathematics, Edinburgh University, Edinburgh, United Kingdom.

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Acknowledgements:

The authors are pleased to acknowledge the assistance of B. L. J. Braaksma with §§16.5 and 16.11.

Notes:

The main references used in writing this chapter are Erdélyi et al. (1953a), Luke (1969a, 1975). For additional bibliographic reading see Appell and Kampé de Fériet (1926), Andrews et al. (1999) and Slater (1966).

Referenced by:

Profile Adri B. Olde Daalhuis, Profile Richard A. Askey, § ‣ Chapter Authors, § ‣ Chapter Authors, § ‣ Associate Editors, Organization and Objective, § ‣ Software Cross Index

Permalink:

http://dlmf.nist.gov/16

Addition (effective with 1.0.11):

The reference Appell and Kampé de Fériet (1926) was added to the Note section.

   

• Notation
  1. 16.1 Special Notation
• Generalized Hypergeometric Functions
  1. 16.2 Definition and Analytic Properties
  2. 16.3 Derivatives and Contiguous Functions
  3. 16.4 Argument Unity
  4. 16.5 Integral Representations and Integrals
  5. 16.6 Transformations of Variable
  6. 16.7 Relations to Other Functions
  7. 16.8 Differential Equations
  8. 16.9 Zeros
  9. 16.10 Expansions in Series of ${}_p{}^{}F_q^{}$ Functions
  10. 16.11 Asymptotic Expansions
  11. 16.12 Products
• Two-Variable Hypergeometric Functions
  1. 16.13 Appell Functions
  2. 16.14 Partial Differential Equations
  3. 16.15 Integral Representations and Integrals
  4. 16.16 Transformations of Variables

• Meijer $G$-Function
  1. 16.17 Definition
  2. 16.18 Special Cases
  3. 16.19 Identities
  4. 16.20 Integrals and Series
  5. 16.21 Differential Equation
  6. 16.22 Asymptotic Expansions
• Applications
  1. 16.23 Mathematical Applications
  2. 16.24 Physical Applications
• Computation
  1. 16.25 Methods of Computation
  2. 16.26 Approximations
  3. 16.27 Software

15.20 Software16.1 Special Notation

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