NEW ANALYSIS OF WITTAKER FUNCTIONS

Abstract

Integrals involving products of two Whittaker functions and Bessel functions are evaluated in §§ 3,4. Also the integrals

\[ \int_0^\infty t^{\rho-1}W_{k_1m}(t)W_{-k_1m}(t)W_{\mu, \nu}\left(\frac{2iz}{t}\right)W_{\mu, \nu}\left(-\frac{2iz}{t}\right)\ dt\]

and

\[ \int_0^\infty t^{\rho-1}W_{k_1m}(t)W_{-k_1m}(t)W_{\mu, \nu}(2zt)W_{-\mu, \nu}(2zt)\ dt\]

are evaluated in § 5 while in § 6 integrals involving the product of three Whittaker functions are established.