Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Convergence of Magnus integral addition theorems for confluent hypergeometric functions



Howard Cohl, Hans Volkmer, Jessica Hirtenstein


In 1946, Magnus presented an addition theorem for the confluent hypergeometric function of the second kind $U$ with argument $x+y$ expressed as an integral of a product of two $U$'s, one with argument $x$ and another with argument $y$. We take advantage of recently obtained asymptotics for $U$ with large complex first parameter to determine a domain of convergence for Magnus' result. Using well-known specializations of $U$, 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.
Integral Transforms and Special Functions


Confluent hypergeometric functions, Bessel functions, Modified parabolic cylinder functions, Integral addition theorems


Cohl, H. , Volkmer, H. and Hirtenstein, J. (2016), Convergence of Magnus integral addition theorems for confluent hypergeometric functions, Integral Transforms and Special Functions, [online],, (Accessed April 15, 2024)
Created June 23, 2016, Updated May 4, 2021