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Expansions for Kν(ξ) involving Airy's function†

Published online by Cambridge University Press:  24 October 2008

James A. Donaldson
James A. Donaldson
Affiliation:
University of Illinois, Chicago Circle
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Abstract

In this note it is shown that the modified Bessel function of arbitrary order may be represented as the sum of two products where one product involves Airy's function and the other product involves the first-order derivative of Airy's function.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 66 , Issue 1 , July 1969 , pp. 91 - 94
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

(1)Donaldson, J. A.Integral representations of the extended Airy integral type for the modified Bessel function. J. Math. and Phys. 46 (1967), 111–114.CrossRefGoogle Scholar
(2)Magnus, W. and Oberhettinger, F., Formulas and theorems for mathematical physics. Chelsea Publishing Co. (New York, 1954).Google Scholar
(3)Mursi, Z.On the relation of the Airy and Allied integrals to the Bessel functions. Proc. Math. Phys. Soc. U.A.R. (Egypt), 3, (1948).Google Scholar