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A new class of Laplace inverses and their applications

โœ Scribed by P.M. Jordan; P. Puri; G. Boros

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
398 KB
Volume
13
Category
Article
ISSN
0893-9659

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โœฆ Synopsis

In this work, a new class of inverse Laplace transforms of exponential functions involving nested square roots are determined. Using these new inverses and other techniques from Laplace transform theory, a new class of three-parameter definite integrals, that yield to exact evaluation, is generated. It is shown that these integrals evaluate to simple closed-form expressions. These results are then verified using independent analytical techniques. Special and limiting cases of the parameters are investigated, some of which yield well-known expressions from classical analysis. Asymptotic results for these integrals and inverses are also given. In addition, a representation of the complementary error function as a limit is presented. Last, some aspects concerning the numerical implementation of these inverses are discussed and several applications in continuum mechanics are noted.

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