Any reference for $ \Gamma(a) U(a,b,z) =\sum_{j=0}^{+\infty} \frac{1}{j+a} L^{b-1}_{j}(z) $

Question

Any reference that we can find the following $$ \Gamma(a) U(a,b,z) =\sum_{j=0}^{+\infty} \frac{1}{j+a} L^{b-1}_{j}(z),$$ where $\Gamma(.)$ is the Gamma's function, $U\left(a, b; z\right)$ is the Kummer's Function of the second kind and $L^{\alpha}_n(z)$ is the generalized Laguerre polinomials.

Thank in advance

Answer 1

This is formula (8) on page 28 of: F.G. Tricomi, Fonctions hypergéométriques confluentes. Mémorial des sciences mathématiques, 140 (1960), p. 1-86. Availabe from http://www.numdam.org/item?id=MSM_1960__140__1_0

Answer 2

1. NIST Digital Library of Mathematical Functions
2. Volume 1 of Higher Transcendental Functions
3. Wolfram Mathworld

Note that names of these functions have not been standardized so there can be some confusion. Kummer function of the second kind are also called Tricomi function or Gordon function. They do fall under the umbrella name of confluent hypergeometric functions of the second kind.