Abstract
A proof of an orthogonality relation for the MacDonald's functions with identical arguments but unequal complex lower indices is presented. The orthogonality is derived first via a heuristic approach based on the Mehler-Fock integral transform of the MacDonald's functions, and then proved rigorously using a polynomial approximation procedure.
| Original language | English |
|---|---|
| Pages (from-to) | 380-390 |
| Number of pages | 11 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 360 |
| Issue number | 2 |
| DOIs | |
| State | Published - Dec 15 2009 |
Funding
E-mail addresses: [email protected] (A. Passian), [email protected] (H. Simpson), [email protected] (S. Kouchekian), [email protected] (S.B. Yakubovich). 1 The work of the first author was supported by the Oak Ridge National Laboratory, Managed by UT-Battelle, LLC for the Department of Energy under contract number DE-AC05-0096OR22725. 2 The research of the third author was partially supported by the National Science Foundation grant DMS–0500916. 3 The work of the fourth author was supported by the “Centro de Mathematica” of the University of Porto.
Keywords
- Kontorovich-Lebedev transform
- Mehler-Fock transform
- Modified Bessel functions