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2008 The Analysis of Contour Integrals
Tanfer Tanriverdi, JohnBryce Mcleod
Abstr. Appl. Anal. 2008: 1-12 (2008). DOI: 10.1155/2008/765920

Abstract

For any n , the contour integral y = cosh n + 1 x C ( cosh ( z s ) / ( sinh z - sinh x ) n + 1 d z, s 2 = - λ , is associated with differential equation d 2 y ( x ) / d x 2 + ( λ + n ( n + 1 ) / cosh 2 x ) y ( x ) = 0 . Explicit solutions for n = 1 are obtained. For n = 1 , eigenvalues, eigenfunctions, spectral function, and eigenfunction expansions are explored. This differential equation which does have solution in terms of the trigonometric functions does not seem to have been explored and it is also one of the purposes of this paper to put it on record.

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Tanfer Tanriverdi. JohnBryce Mcleod. "The Analysis of Contour Integrals." Abstr. Appl. Anal. 2008 1 - 12, 2008. https://doi.org/10.1155/2008/765920

Information

Published: 2008
First available in Project Euclid: 9 September 2008

zbMATH: 1182.34018
MathSciNet: MR2393117
Digital Object Identifier: 10.1155/2008/765920

Rights: Copyright © 2008 Hindawi

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