Digital Library of Mathematical Functions
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14 Legendre and Related FunctionsComplex Arguments

§14.26 Uniform Asymptotic Expansions

The uniform asymptotic approximations given in §14.15 for Pν-μ(x) and Qνμ(x) for 1<x< are extended to domains in the complex plane in the following references: §§14.15(i) and 14.15(ii), Dunster (2003b); §14.15(iii), Olver (1997b, Chapter 12); §14.15(iv), Boyd and Dunster (1986). For an extension of §14.15(iv) to complex argument and imaginary parameters, see Dunster (1990b).

See also Frenzen (1990), Gil et al. (2000), Shivakumar and Wong (1988), Ursell (1984), and Wong (1989) for uniform asymptotic approximations obtained from integral representations.