Abstract and Applied Analysis
Volume 2008 (2008), Article ID 765920, 12 pages
doi:10.1155/2008/765920
The analysis of contour integrals
Tanfer Tanriverdi1
and Johnbryce McLeod2
1Department of Mathematics, Harran University, Osmanbey Campus, Sanlurfa 63100, Turkey
2Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA 15260, USA
Abstract
For any n, the contour integral y=coshn+1x∮C(cosh(zs)/(sinhz-sinhx)n+1dz,s2=-λ, is associated with differential equation d2y(x)/dx2+(λ+n(n+1)/cosh2x)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.