A generalization of the Airy integral for 𝑓”-𝑧ⁿ𝑓=0

Gundersen, Gary G.; Steinbart, Enid M.

doi:10.1090/S0002-9947-1993-1149123-3

A generalization of the Airy integral for $f”-z^ nf=0$
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by Gary G. Gundersen and Enid M. Steinbart PDF

Trans. Amer. Math. Soc. 337 (1993), 737-755 Request permission

Abstract:

It is well known that the Airy integral is a solution of the Airy differential equation $f'' - zf = 0$ and that the Airy integral is a contour integral function with special properties. We show that there exist analogous special contour integral solutions of the more general equation $f'' - {z^n}f = 0$ where $n$ is any positive integer. Related results are given.

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