Laplace transform of products of Bessel functions: A visitation of earlier formulas

Authors:
Eduardo Kausel and Mirza M. Irfan Baig

Journal:
Quart. Appl. Math. **70** (2012), 77-97

MSC (2010):
Primary 44-00, 44A10, 74-00

Published electronically:
September 16, 2011

MathSciNet review:
2920617

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Abstract | References | Similar Articles | Additional Information

Abstract: This note deals with the Laplace transforms of integrands of the form , which are found in numerous fields of application. Specifically, we provide herein both a correction and a supplement to the list of integrals given in 1997 by Hanson and Puja, who in turn extended the formulas of Eason, Noble and Sneddon of 1956. The paper concludes with an extensive tabulation for particular cases and range of parameters.

**1.**M. Abramovitz and I. Stegun.*Handbook of Mathematical Functions with Formulas*, Tenth Printing. Graphs, and Mathematical Tables, U.S. National Bureau of Standards, 1972.**2.**Paul F. Byrd and Morris D. Friedman,*Handbook of elliptic integrals for engineers and scientists*, Die Grundlehren der mathematischen Wissenschaften, Band 67, Springer-Verlag, New York-Heidelberg, 1971. Second edition, revised. MR**0277773****3.**G. Eason, B. Noble, and I. N. Sneddon,*On certain integrals of Lipschitz-Hankel type involving products of Bessel functions*, Philos. Trans. Roy. Soc. London. Ser. A.**247**(1955), 529–551. MR**0069961****4.**I. S. Gradshteyn and I. M. Ryzhik,*Table of integrals, series, and products*, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London-Toronto, Ont., 1980. Corrected and enlarged edition edited by Alan Jeffrey; Incorporating the fourth edition edited by Yu. V. Geronimus [Yu. V. Geronimus] and M. Yu. Tseytlin [M. Yu. Tseĭtlin]; Translated from the Russian. MR**582453****5.**Mark T. Hanson and Igusti W. Puja,*The evaluation of certain infinite integrals involving products of Bessel functions: a correlation of formula*, Quart. Appl. Math.**55**(1997), no. 3, 505–524. MR**1466145****6.**A.E.H. Love. (1929).*The stress produced in a semi-infinite solid by pressure on part of the boundary*, Philosophical Transactions of the Royal Society of London, Series A, 228, pp. 377-420, 1929.**7.**Fritz Oberhettinger and Larry Badii,*Tables of Laplace transforms*, Springer-Verlag, New York-Heidelberg, 1973. MR**0352889**

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Additional Information

**Eduardo Kausel**

Affiliation:
Professor of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

Email:
kausel@mit.edu

**Mirza M. Irfan Baig**

Affiliation:
Simpson, Gumpertz & Heger Inc., Waltham, Massachusetts 02453

Email:
irfan.baig@gmail.com

DOI:
http://dx.doi.org/10.1090/S0033-569X-2011-01239-2

Received by editor(s):
June 2, 2010

Published electronically:
September 16, 2011

Article copyright:
© Copyright 2011
Brown University

The copyright for this article reverts to public domain 28 years after publication.