On Some Families of New Constructed Polynomials
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The purpose of this paper is to introduce some new polynomials obtained from second- and third-order algebraic equations by using a simple iterative method. One-variable polynomials obtained in this study deal with special form of Pöschl–Teller potential with constant energy, and the two-variable polynomials are related to time-dependent wave equations. We present some recurrence relations, Binet formula and get various families of linear, multilinear and multilateral generating functions for these polynomials. In addition, we derive some special cases. At the end of the paper we also give an extension to the multidimensional case of our results.
KeywordsGenerating function Recurrence relation Hypergeometric function Gauss equation
Mathematics Subject Classification33C05
The authors would like to thank the reviewers for carefully reading the manuscript and providing valuable comments.