Finding all Bessel type solutions for linear differential equations
A linear differential equation with rational function coefficients has a Bessel type solution when it is solvable in terms of Bessel functions Bv(x), derivative, change of variables x->f(x), algebraic operations and exponential integrals. For second order equations with rational function coefficients, f must be a rational function or the square root of a rational function. Previous work has demonstrated how to compute Bessel type solutions if an only if f is a rational function. However, the extension to generality is under explored, particularly when f is the square root of a rational function. In this talk we will demonstrate a complete algorithm to find all the Bessel type solutions for linear differential equations. The algorithm is illustrated with application using Maple.