For ℜ[μ + ν]>0, left bracketing bar arg p right bracketing bar <π/4, and a>0, integral_0^∞ J_ν(a t) e^(-p^2 t^2) t^(μ - 1) d t = (a/(2p))^ν (Γ[1/2(ν + μ)])/(2p^μ Γ(ν + 1)) _1 F_1(1/2(ν + μ);ν + 1; - a^2/(4p^2)), where J_ν(z) is a Bessel function of the first kind, Γ(z) is the gamma function, and _1 F_1(a;b;z) is a confluent hypergeometric function of the first kind.
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