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

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, \({}_0F_1\)

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