Chapter 13Confluent Hypergeometric Functions
A. B. Olde DaalhuisSchool of Mathematics,Edinburgh University,Edinburgh, United Kingdom.
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- Acknowledgements:
- This chapter is based in part onAbramowitz and Stegun (1964, Chapter 13) by L.J. Slater. The author isindebted to J. Wimp for several references.
- Notes:
- The main references used in writing this chapter areBuchholz (1969),Erdélyi et al. (1953a),Olver (1997b),Slater (1960), andTemme (1996b). For additionalbibliographic reading seeAndrews et al. (1999),Hochstadt (1971),Luke (1969a,b),Wang and Guo (1989), andWhittaker and Watson (1927).
- Referenced by:
- §16.18,§18.17(v),§18.17(vi),§3.10(ii),Ch.33,ProfileAdri B. Olde Daalhuis,§ ‣Chapter Authors,§ ‣Associate Editors,§ ‣Software Cross Index
- Permalink:
- http://dlmf.nist.gov/13
- Notation
- Kummer Functions
- 13.2Definitions and Basic Properties
- 13.3Recurrence Relations and Derivatives
- 13.4Integral Representations
- 13.5Continued Fractions
- 13.6Relations to Other Functions
- 13.7Asymptotic Expansions for Large Argument
- 13.8Asymptotic Approximations for Large Parameters
- 13.9Zeros
- 13.10Integrals
- 13.11Series
- 13.12Products
- 13.13Addition and Multiplication Theorems
- Whittaker Functions
- 13.14Definitions and Basic Properties
- 13.15Recurrence Relations and Derivatives
- 13.16Integral Representations
- 13.17Continued Fractions
- 13.18Relations to Other Functions
- 13.19Asymptotic Expansions for Large Argument
- 13.20Uniform Asymptotic Approximations for Large
- 13.21Uniform Asymptotic Approximations for Large
- 13.22Zeros
- 13.23Integrals
- 13.24Series
- 13.25Products
- 13.26Addition and Multiplication Theorems
