Integrals of some three Bessel functions and Legendre functions. II

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Abstract
Integrals of three Bessel functions of the form ∫∞0Jμ(at)Jν(bt) ×H(1)ρ(ct)dt are calculated when μ,ν,ρ,a,b, and c are arbitrary real numbers. For this, use is made of the factorization of the Appell function F4 in two hypergeometric functions. Further simplifications occur if μ=±ν or ρ=±1/2. New results are given, mainly when real a, b, and c satisfy the inequalities ‖a−b‖<c<a+b, which correspond to most physical situations.

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