Duran, U.; Acikgoz, M.; Araci, S. Construction of the Type 2 Poly-Frobenius–Genocchi Polynomials with Their Certain Applications. Advances in Difference Equations, 2020, 2020. https://doi.org/10.1186/s13662-020-02889-2.
Duran, U.; Acikgoz, M.; Araci, S. Construction of the Type 2 Poly-Frobenius–Genocchi Polynomials with Their Certain Applications. Advances in Difference Equations, 2020, 2020. https://doi.org/10.1186/s13662-020-02889-2.
Duran, U.; Acikgoz, M.; Araci, S. Construction of the Type 2 Poly-Frobenius–Genocchi Polynomials with Their Certain Applications. Advances in Difference Equations, 2020, 2020. https://doi.org/10.1186/s13662-020-02889-2.
Duran, U.; Acikgoz, M.; Araci, S. Construction of the Type 2 Poly-Frobenius–Genocchi Polynomials with Their Certain Applications. Advances in Difference Equations, 2020, 2020. https://doi.org/10.1186/s13662-020-02889-2.
Abstract
Motivated by the definition of the type 2 poly-Bernoulli polynomials introduced by Kim-Kim, in the present paper, we consider a class of new generating function for the Frobenius-Genocchi polynomials, called the type 2 poly-Frobenius-Genocchi polynomials, by means of the polyexponential function. Then, we derive some useful relations and properties. We show that the type 2 poly-Frobenius-Genocchi polynomias equal a linear combination of the classical Frobenius-Genocchi polynomials and Stirling numbers of the first kind. In a special case, we give a relation between the type 2 poly-Frobenius-Genocchi polynomials and Bernoulli polynomials of order k. Moreover, inspired by the definition of the unipoly-Bernoulli polynomials introduced by Kim-Kim, we introduce the unipoly-Frobenius-Genocchi polynomials by means of unipoly function and give multifarious properties including derivative and integral properties. Furthermore, we provide a correlation between the unipoly-Frobenius-Genocchi polynomials and the classical Frobenius-Genocchi polynomials.
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
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