On the derivatives of the Bessel and Struve functions with respect to the order

Abstract

Closed form expressions are obtained for the first derivatives with respect to the order of the Bessel functions J ν(z), Y ν(z), I ν(z), K ν(z); integral Bessel functions Ji ν(z), Yi ν(z), Ki ν(z); and Struve functions Hν(z), Lν(z) at ν = ±n, ν = ±n + 1/2, with n = 0, 1, 2….