Combinatorics of Jacobi-configurations. III: The Srivastava-Singhal generating function revisited
[Part I, Lect. Notes Math. 1234, 294-307 (1986; Zbl 0632.05012); part II, Act. Sém. Lotharing. Comb., Bologne 1985, 113-133 (1986)]. The author gives a combinatorial proof and a multivariable generalization of Jacobi's generating function for the Jacobi polynomials. The initial proof was presented by \textit{H. M. Srivastava} and \textit{J. P. Singhal} [J. Math. Anal. Appl. 41, 748-752 (1973; Zbl 0218.33006)]. In this work an extension of the approach of \textit{D. Foata} and \textit{P. Leroux} [Proc. Am. Math. Soc. 87, 47-53 (1983; Zbl 0522.33004)] is applied, using the language of ``species of structures'' - endofunctions, trees and contractions.
scientific article; zbMATH DE number 4099309
scientific article