Asymptotic Series Evaluation of Integrals Arising in the Particular Solutions to Airy’s Inhomogeneous Equation with Special Forcing Functions-Reference-Cited by-同舟云学术

Asymptotic Series Evaluation of Integrals Arising in the Particular Solutions to Airy’s Inhomogeneous Equation with Special Forcing Functions

Published:2022-05-31 Issue: Volume:21 Page:303-308
ISSN:2224-2880
Container-title:WSEAS TRANSACTIONS ON MATHEMATICS
language:en
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Author:

Hamdan M. H.¹,Dajani S. Jayyousi²,Roach D. C.³

Affiliation:

1. Department of Mathematics and Statistics, University of New Brunswick 100 Tucker Park Road, Saint John, New Brunswick, E2L 4L5 CANADA

2. Department of Mathematics and Computer Science Lake Forest College Lake Forest, IL 60045 USA

3. Department of Engineering, University of New Brunswick 100 Tucker Park Road, Saint John, New Brunswick, E2L 4L5 CANADA

Abstract

In this work, particular and general solutions to Airy’s inhomogeneous equation are obtained when the forcing function is one of Airy’s functions of the first and second kind, and the standard Nield-Kuznetsov function of the first kind. Particular solutions give rise to special integrals that involve products of Airy’s and Nield-Kuznetsov functions. Evaluation of the resulting integrals is facilitated by expressing their integrands in asymptotic series. Corresponding expressions for the Nield-Kuznetsov function of the second kind are obtained.

Publisher

World Scientific and Engineering Academy and Society (WSEAS)

Subject

General Mathematics

Reference16 articles.

1. Airy, G.B. (1838). On the intensity of light in the neighbourhood of a caustic. Trans. Cambridge Phil. Soc., Vol. 6, 1838, pp. 379-401.

2. Abramowitz, M. and Stegun, I.A., Handbook of Mathematical Functions, Dover, New York, 1984.

3. Vallée, O. and Soares, M., Airy functions and applications to Physics. World Scientific, London, 2004.

4. Hamdan, M.H. and Kamel, M.T., On the Ni(x) integral function and its application to the Airy's non homogeneous equation. Applied Math. Comput., Vol. 21(17), 2011, pp. 7349-7360.

5. Temme, N.M., Special Functions: An Introduction to the Classical Functions of Mathematical Physics, Wiley, New York, 1996.

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