Polynomials defined by generating relations

Abstract

Abstact. Various authors have made efforts for finding new generating functions for known polynomial sets. In the present paper, by making use of the operator Tk = x(k + xD), a number of generating functions and characterizations have been obtained for various polynomials in a systematic manner.

Some polynomials defined by generating relations

“…Introduction. Recently, H. B. Mittal [6] demonstrated some applications of the differential operator A closer look at the defining relation (4) would evidently expose a number of superfluous parameters on its right-hand side. For instance, one can replace, without any loss of generality, x by ((-l)qx/c)l^p~q^.…”

“…Corresponding to the power series \p(u) given by (3), let ln,q](-ri)k(l + a + (ß+l)n)Xk (6) Sia>ß)(\-x)= y ---Tfc* » W **t<M> ¿L (l + a + ßn\x+q)k where a, ß and X are arbitrary constants, real or complex, and q is an arbitrary positive integer.…”