PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 33(47), pp. 315 (1983) 

A UNIFIED CLASS OF POLYNOMIALSHukum Chand AgrawalDepartment of Mathematics, Lucknow University, Lucknow, IndiaAbstract: In this paper we propose to study the polynomial set $\left\{f^{(\alpha)}_n\right\}(x)$ satisfying the functional relation $$ T(\Delta_\alpha)\left\{f^{(\alpha)}_n(x)\right\}= f^{(\alpha+1)}_{n1}(x), \qquad n=1,2,3,\dots, $$ where $f(\alpha)_n(x)$ is the polynomial of degree $n$ in $x$ and $T$ is the operator of infinite order defined by $$ T(\Delta_\alpha)= \sum_{k=0}^\infty h_k^{(\alpha)}\Delta_\alpha^{k+1}, \enskip h_0^{(\alpha)}\neq 0, $$ in which $\Delta_\alpha \{f(\alpha)\}= f(\alpha+1)f(\alpha)$. Full text of the article:
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