Two Definite Integrals Involving Products of Four Legendre Functions
Abstract
The definite integrals ∫-11x[P(x)]4\,d x and ∫01x[P(x)]2\[P(x)]2-[P(-x)]2\\,d x are evaluated in closed form, where P stands for the Legendre function of degree ∈ C. Special cases of these integral formulae have appeared in arithmetic studies of automorphic Green's functions and Epstein zeta functions.
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