Chapter 15 Hypergeometric Function
A. B. Olde Daalhuis
Affiliation: School of Mathematics,
Edinburgh University,
Edinburgh, United Kingdom.
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- Acknowledgements:
- This chapter is based in part on Chapter 15 of Abramowitz and Stegun (1964) by Fritz Oberhettinger. The author thanks Richard Askey and Simon Ruijsenaars for many helpful recommendations.
- Notes:
- The main references used in writing this chapter are Andrews et al. (1999) and Temme (1996b). For additional bibliographic reading see Erdélyi et al. (1953a), Hochstadt (1971), Luke (1969a), Olver (1997b), Slater (1966), Wang and Guo (1989), and Whittaker and Watson (1927).
- Referenced by:
- §16.18, Profile Adri B. Olde Daalhuis, § ‣ Chapter Authors, § ‣ Associate Editors, Erratum (V1.0.28) for Chapters 14 Legendre and Related Functions, 15 Hypergeometric Function, § ‣ Software Cross Index
- Permalink:
- http://dlmf.nist.gov/15
- Notation
-
Properties
- 15.2 Definitions and Analytical Properties
- 15.3 Graphics
- 15.4 Special Cases
- 15.5 Derivatives and Contiguous Functions
- 15.6 Integral Representations
- 15.7 Continued Fractions
- 15.8 Transformations of Variable
- 15.9 Relations to Other Functions
- 15.10 Hypergeometric Differential Equation
- 15.11 Riemann’s Differential Equation
- 15.12 Asymptotic Approximations
- 15.13 Zeros
- 15.14 Integrals
- 15.15 Sums
- 15.16 Products
- Applications
- Computation
