On the integration of products of Whittaker functions with respect to the second index
Abstract
Several new formulas are developed that enable the evaluation of a family of definite integrals containing the product of two Whittaker W-functions. The integration is performed with respect to the second index, and the first index is permitted to have any complex value, within certain restrictions required for convergence. The method utilizes complex contour integration along with various symmetry relations satisfied by the Whittaker functions. The new results derived in this paper are complementary to the previously known integrals of products of Whittaker functions, which generally treat integration with respect to either the first index or the primary argument. A physical application involving radiative transport is discussed.
Keywords
Cite
@article{arxiv.math-ph/0310048,
title = {On the integration of products of Whittaker functions with respect to the second index},
author = {Peter A. Becker},
journal= {arXiv preprint arXiv:math-ph/0310048},
year = {2015}
}
Comments
Accepted for publication in the Journal of Mathematical Physics