A Note on a Multilinear Generating Function for the Konhauser Biorthogonal Polynomials

Abstract

It is observed, in the present note, that a multilinear generating function for the Konhauser biorthogonal polynomials $Y_n^\alpha (x;k)$ and $Z_n^\alpha (x;k)$, which is the main result of a recent paper by K. R. Patil and N. K. Thakare [SIAM J. Math. Anal., 9 (1978), pp. 921–923], does not hold true as asserted in the literature. The corrected (and slightly improved) version of this result is given and its relationship with an obvious special case of a known multilinear generating function (due to H. M. Srivastava and J. P. Singhal [Acad. Roy. Belg. Bull. Cl. Sci. (5), 58 (1972), pp. 1238–1247]) for a certain class of generalized hypergeometric polynomials is indicated.