relation to associated Legendre functions
(0.006 seconds)
1—10 of 28 matching pages
1: 14.3 Definitions and Hypergeometric Representations
§14.3 Definitions and Hypergeometric Representations
… ►§14.3(ii) Interval
… ►§14.3(iii) Alternative Hypergeometric Representations
… ►
14.3.14
…
►
§14.3(iv) Relations to Other Functions
…2: 14.7 Integer Degree and Order
…
►
§14.7(i)
…3: 14.5 Special Values
4: 15.9 Relations to Other Functions
…
►
§15.9(iv) Associated Legendre Functions; Ferrers Functions
…5: 30.6 Functions of Complex Argument
…
►
Relations to Associated Legendre Functions
…6: 14.2 Differential Equations
…
►Ferrers functions and the associated Legendre functions are related to the Legendre functions by the equations , , , , .
…
7: 14.21 Definitions and Basic Properties
…
►
§14.21(i) Associated Legendre Equation
… ►Standard solutions: the associated Legendre functions , , , and . … ►§14.21(ii) Numerically Satisfactory Solutions
… ►§14.21(iii) Properties
…8: 14 Legendre and Related Functions
Chapter 14 Legendre and Related Functions
…9: 16.18 Special Cases
§16.18 Special Cases
… ►This is a consequence of the following relations: …As a corollary, special cases of the and functions, including Airy functions, Bessel functions, parabolic cylinder functions, Ferrers functions, associated Legendre functions, and many orthogonal polynomials, are all special cases of the Meijer -function. Representations of special functions in terms of the Meijer -function are given in Erdélyi et al. (1953a, §5.6), Luke (1969a, §§6.4–6.5), and Mathai (1993, §3.10).10: 34.3 Basic Properties: Symbol
…
►