Partial Derivative Equations and Identities for Hermite-Based Peters-Type Simsek Polynomials and Their Applications

Eda Yuluklu ()
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Eda Yuluklu: Department of Mathematics, Faculty of Engineering and Natural Sciences, Usak University, 1 Eylul Campus, Usak 64200, Turkey

Mathematics, 2024, vol. 12, issue 16, 1-12

Abstract: The objective of this paper is to investigate Hermite-based Peters-type Simsek polynomials with generating functions. By using generating function methods, we determine some of the properties of these polynomials. By applying the derivative operator to the generating functions of these polynomials, we also determine many of the identities and relations that encompass these polynomials and special numbers and polynomials. Moreover, using integral techniques, we obtain some formulas covering the Cauchy numbers, the Peters-type Simsek numbers and polynomials of the first kind, the two-variable Hermite polynomials, and the Hermite-based Peters-type Simsek polynomials.

Keywords: generating functions; special numbers and polynomials; two-variable Hermite polynomials; Peters-type Simsek numbers and polynomials; Hermite-type combinatorial Simsek polynomials (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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