Indefinite integrals of Bessel and Struve functions with half-integer indices, and incomplete gamma functions with integer indices, all times $Exp(-ax^{2})$ and divided by powers

Abstract

Indefinite integrals are found for 63 half-integer Bessel and Struve functions, and incomplete gamma functions with integer indices, each multiplied by $Exp(-ax^{2})$ and divided by powers. A series solution is given for the individual terms (of any inverse power) in such functions, split into even and odd portions. Eight integrals are given involving these series.