A new class of generalized polynomials associated with Milne-Thomson-based poly-Bernoulli polynomials

Khan, Waseem Ahmad and Srivastava, Divesh and Nisar, Kottakkaran Sooppy (2024) A new class of generalized polynomials associated with Milne-Thomson-based poly-Bernoulli polynomials. Miskolc Mathematical Notes, 25 (2). pp. 793-803. ISSN 1787-2413

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Abstract

Motivated by their importance and potential for applications in certain problems in number theory, combinatorics, classical and numerical analysis, and other field of applied mathematics, a variety of polynomials and numbers with their variants and extensions have recently been introduced and investigated. In this sequel, we modify the known generating functions of polynomials, due to both Milne-Thomson and Dere and Simsek, to introduce a new class of generalized polynomials and present some of their involved properties. As obvious special cases of the newly introduced polynomials, we also called power sum-Laguerre-Hermite polynomials and generalized Laguerre and poly-Bernoulli polynomials and present some of their involved identities and formulas. The results presented here, being very general, are pointed out to be specialized to yield a number of known and new identities involving relatively simple and familiar polynomials.

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