Repeated integrals and derivatives of K Bessel functions. (English) Zbl 0671.33006

Amos, Donald E.

SIAM J. Math. Anal. 20, No. 2, 169-175 (1989).

Repeated integrals of the modified Bessel function \(K_{\nu}(x)\) on \(0<x<\infty\) are considered. Earlier results with \(\nu =0\) (in that case the integrals are called Bickley functions) are extended; also, repeated differentiations are considered. Expansions are given in terms of exponential integrals, together with inversion relations for such expansions.

Reviewer: N.M.Temme

MSC:

33C10

Bessel and Airy functions, cylinder functions, \({}_0F_1\)

Keywords:

modified Bessel function; Bickley functions; exponential integrals

Software:

BSKIN