On New Identities for Basic Polynomials Sequences in Finite Operator Calculus
A. Maheswaran *
Department of Mathematical Sciences, Cardamom Planters' Association College, Bodinayakanur, Tamilnadu 625513, India.
C. Elango
Department of Mathematical Sciences, Cardamom Planters' Association College, Bodinayakanur, Tamilnadu 625513, India.
*Author to whom correspondence should be addressed.
Abstract
The main objective of this paper is to investigate the characterization of the delta operator for some basic polynomials. A theorem from G.C.Rota which gives the necessary and sufficient conditions for the sequence of basic polynomials corresponding to some delta operator Q is reconstructed in terms of three new identities and this theorem is verified by some comprehensive examples.
Keywords: Delta operator, basic polynomial sequences, binomial type sequences