An Integral Transform Involving Heun Functions and a Related Eigenvalue Problem
- 1 May 1986
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Mathematical Analysis
- Vol. 17 (3) , 688-703
- https://doi.org/10.1137/0517049
Abstract
An integral transform involving Heun functions is obtained. When combined with the explicit solutions given by Carlitz new closed integral representations are obtained for some Heun functions. As an application we solve an eigenvalue problem related to birth and death processes obtaining the exact spectrum and eigenfunctions. A direct proof of their orthogonality and completeness is given.Keywords
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