Bateman Function

for , where  is a confluent hypergeometric function of the second kind.

REFERENCES:

Bateman, H. "The -Function, a Particular Case of the Confluent Hypergeometric Function." Trans. Amer. Math. Soc. 33, 817-831, 1931.

Koepf, W. Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities. Braunschweig, Germany: Vieweg, p. 179, 1998.

Koepf, W. and Schmersau, D. "Bounded Nonvanishing Functions are Bateman Functions." Complex Variables 25, 237-259, 1994.