Generating Functions of a New Class of Semi-Orthogonal Polynomials \(X_n (x ; a,α)\) Using Lie Group Theory - Jagtap, R. R.; Andhare, P. G.; Gaikwad, S. B. (Communications in Mathematics and Applications, 2025)
In this paper, by applying the group theoretic method introduced by Weisner, we determined new generating relations of a new class of semi-orthogonal polynomials \(X_{n} (x;a,α)\). By giving proper analytical reasoning to the index \(m\) of the semi-orthogonal polynomial, we derived three linear partial differential operators with the help of the ascending and descending differential recurrence relation of the polynomial. These linear partial differential operators generate a Lie group.
Keywords: \(X_n\) polynomials; Generating functions; Weisner method