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Zbl 0671.33006
Amos, Donald E.
Repeated integrals and derivatives of K Bessel functions. (English)
[J] SIAM J. Math. Anal. 20, No.2, 169-175 (1989). ISSN 0036-1410; ISSN 1095-7154/e

Repeated integrals of the modified Bessel function $K\sb{\nu}(x)$ 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.
[N.M.Temme]

MSC 2000:: *33C10 Cylinder functions, etc.

Keywords: modified Bessel function; Bickley functions; exponential integrals

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