Article ID: MTJPAM-D-23-00002

Title: Identities for the multiparametric higher-order Hermite-based Peters-type Simsek polynomials of the first kind


Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-23-00002; Volume 5 / Issue 1 / Year 2023, Pages 102-123

Document Type: Research Paper

Author(s): Irem Kucukoglu a

aDepartment of Engineering Fundamental Sciences, Alanya Alaaddin Keykubat University TR-07425 Antalya, Turkey

Received: 14 March 2023, Accepted: 13 August 2023, Published: 13 September 2023

Corresponding Author: Irem Kucukoglu (Email address: irem.kucukoglu@alanya.edu.tr)

Full Text: PDF

Abstract

The main aim of this study is to investigate the multiparametric higher-order Hermite-based Peters-type Simsek numbers and polynomials of the first kind, which were introduced by the author in her recent paper [18]. To achieve this aim, we first provide pseudocodes for symbolic computation of these numbers and polynomials. Moreover, we implement these pseudocodes in the Wolfram language. By these implementations, we provide some tables and plots regarding these numbers and polynomials in some arbitrarily chosen special cases. By using their generating functions with their functional equations, we derive some finite sums, identities and derivative formulas concerning these numbers and polynomials. We also investigate the first order multiparametric Hermite-based Peters-type Simsek polynomials and we provide some remarks and observations about their some reductions. Finally, we conclude the paper by providing some remarks and open problems on the potential applications that could emerge from the Sheffer-type sequences, the heat-type equations, the orthogonality and the analytic continuation.

Keywords: Binomial coefficients, combinatorial numbers and polynomials, computational implementations, finite sums, generating functions, heat-type equations, Hermite polynomials, orthogonal polynomials, Peters polynomials, Sheffer sequences, special numbers and polynomials, two variable Simsek polynomials

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