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