Infinite Integrals Involving Three Spherical Bessel Functions

The integrals ∫₀^∞ tⁿ jl₁ (at)jl₂ (bt)jl₃ (ct)dt are calculated, where Jₗ is the spherical Bessel function for any integer indices n, l₁, l₂, l₃ and real positive parameters a, b, c using two different methods. In the first n + l₁ + l₂ + l₃ must be an even integer but the techniques may be generalized to ordinary Bessel functions with noninteger indices. The second method does not depend on the parity of n + l₁ + l₂ + l₃ but remains valid only for integer indices.