On the integration of products of Whittaker functions with respect to the second index

Several new formulas are developed that enable the evaluation of a family of definite integrals containing the product of two Whittaker Wk ,m(x)-functions. The integration is performed with respect to the second index m, and the first index k 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 article are complementary to the previously known integrals of products of Whittaker functions, which generally treat integration with respect to either the first index k or the primary argument x. A physical application involving radiative transport is discussed. © 2004 American Institute of Physics. @DOI: 10.1063/1.1634351#