Confluent Hypergeometric Limit Function

(1)

It has a series expansion

(2)

and satisfies

(3)

It is implemented in the Wolfram Language as Hypergeometric0F1[b, z].

A Bessel function of the first kind can be expressed in terms of this function by

(4)

(Petkovšek et al. 1996).

REFERENCES:

Petkovšek, M.; Wilf, H. S.; and Zeilberger, D. A=B. Wellesley, MA: A K Peters, p. 38, 1996.