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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A generalization of the Airy integral for $ f''-z\sp nf=0$


Authors: Gary G. Gundersen and Enid M. Steinbart
Journal: Trans. Amer. Math. Soc. 337 (1993), 737-755
MSC: Primary 34A20; Secondary 30D35, 33E30
MathSciNet review: 1149123
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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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DOI: https://doi.org/10.1090/S0002-9947-1993-1149123-3
Keywords: Airy differential equation, Airy integral, linear differential equation, contour integral solution
Article copyright: © Copyright 1993 American Mathematical Society