Computation with Three-Term, Linear, Nonhomogeneous Recursion Relations

The problem of stable computation by forward and backward recursion on three-term, linear, nonhomogeneous recursion relations is outlined. The backward recursive theory is applied to integrals commonly arising in mathematical physics, including incomplete Laplace transforms of some Bessel functions, transforms of repeated integrals of the error function, moments of some Bessel functions, and the incomplete gamma function.