Chapter 14 Legendre and Related Functions
- Acknowledgments:
- This chapter is based in part on Abramowitz and Stegun (1964, Chapter 8) by Irene A. Stegun. The author is indebted to Richard Paris for correcting a long-standing error in Eq. (14.18.3) in previous literature.
- Notes:
- The main reference used in writing this chapter is Olver (1997b). For additional bibliographic reading see Erdélyi et al. (1953a, Chapter III), Hobson (1931), Jeffreys and Jeffreys (1956), MacRobert (1967), Magnus et al. (1966), Robin (1957, 1958, 1959), Snow (1952), Szegö (1967), Temme (1996b), and Wong (1989).
- Referenced by:
- ¶ ‣ §18.3, T. Mark Dunster, § ‣ § Software Cross Index
- Permalink:
- http://dlmf.nist.gov/14
Department of Mathematics and Statistics,
San Diego State University,
San Diego, California.
- Notation
-
Real Arguments
- 14.2 Differential Equations
- 14.3 Definitions and Hypergeometric Representations
- 14.4 Graphics
- 14.5 Special Values
- 14.6 Integer Order
- 14.7 Integer Degree and Order
- 14.8 Behavior at Singularities
- 14.9 Connection Formulas
- 14.10 Recurrence Relations and Derivatives
- 14.11 Derivatives with Respect to Degree or Order
- 14.12 Integral Representations
- 14.13 Trigonometric Expansions
- 14.14 Continued Fractions
- 14.15 Uniform Asymptotic Approximations
- 14.16 Zeros
- 14.17 Integrals
- 14.18 Sums
- 14.19 Toroidal (or Ring) Functions
- 14.20 Conical (or Mehler) Functions
- Complex Arguments
- Applications
- Computation