Some new generating relations for certain polynomial systems involving the H-functions (Q1063756)

Starting from an interesting formula of \textit{L. Carlitz} [SIAM J. Math. Anal. 8, 518-532 (1977; Zbl 0357.33004)], involving the classical Laguerre polynomials, the author derives a class of generating relations for certain polynomial systems associated with the H-function of \textit{Ch. Fox} [Trans. Am. Math. Soc. 98, 395-429 (1961; Zbl 0096.308)]. His main result (Theorem 1) and its extension (Theorem 2) involving the familiar H-function of several variables due to the reviewer and \textit{R. Panda} [J. Reine Angew. Math. 283/284, 265-274 (1976; Zbl 0315.33003)] provide generalizations to various earlier results given, for example, by the reviewer and \textit{R. G. Buschman} [Trans. Am. Math. Soc. 205, 360-370 (1975; Zbl 0288.33027); ibid. 226, 393-394 (1977; Zbl 0348.33009)] and by the reviewer and \textit{R. K. Raina} [Hokkaido Math. J. 10, 34-45 (1981; Zbl 0438.33005)].