DOI: 10.2298/aadm250722029h ISSN: 1452-8630

Generalization of Hermite based second kind Peters-type Simsek polynomials

Neslihan Hepsisler, Bayram Çekim, Mehmet Özarslan
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In this study, a generalization of the Hermite based second kind Peters-type Simsek polynomials is introduced. By means of the generating function, an explicit formula, summation formulas, a recurrence relation and a determinant representation are obtained. Using differential and integral operators, relations with the Stirling, Cauchy and Peters-type Simsek numbers are established. Two subfamilies, namely the three-variable and the parametric ones, are also defined, and their graphs and real roots are analyzed.

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