Convergence of Magnus integral addition theorems for confluent hypergeometric functions.

In 1946, Magnus presented an addition theorem for the confluent hypergeometric function of the second kindUwith argumentx+yexpressed as an integral of a product of twoU's, one with argumentxand another with argumenty. We take advantage of recently obtained asymptotics forUwith large complex first parameter to determine a domain of convergence for Magnus' result. Using well-known specializations ofU, we obtain corresponding integral addition theorems with precise domains of convergence for modified parabolic cylinder functions, and Hankel, Macdonald, and Bessel functions of the first and second kind with order zero and one. [ABSTRACT FROM PUBLISHER]