Buchholz polynomials: a family of polynomials relating solutions of confluent hypergeometric and Bessel equations

摘要

The expansion given by H. Buchholz, that allows one to express the regular confluent hypergeometric function M(a,b,z) as a series of modified Bessel functions with polynomial coefficients, is generalized to any solution of the confluent hypergeometric equation, by using a differential recurrence obeyed by the Buchholz polynomials.