Version 1
: Received: 19 August 2019 / Approved: 20 August 2019 / Online: 20 August 2019 (11:29:03 CEST)
How to cite:
Khan, W.; Khan, I.A.; Duran, U.; Acikgoz, M. Certain Results on (p,q)-Hermite Based Apostol Type Frobenius-Euler Polynomials. Preprints2019, 2019080216. https://doi.org/10.20944/preprints201908.0216.v1
Khan, W.; Khan, I.A.; Duran, U.; Acikgoz, M. Certain Results on (p,q)-Hermite Based Apostol Type Frobenius-Euler Polynomials. Preprints 2019, 2019080216. https://doi.org/10.20944/preprints201908.0216.v1
Khan, W.; Khan, I.A.; Duran, U.; Acikgoz, M. Certain Results on (p,q)-Hermite Based Apostol Type Frobenius-Euler Polynomials. Preprints2019, 2019080216. https://doi.org/10.20944/preprints201908.0216.v1
APA Style
Khan, W., Khan, I.A., Duran, U., & Acikgoz, M. (2019). Certain Results on (p,q)-Hermite Based Apostol Type Frobenius-Euler Polynomials. Preprints. https://doi.org/10.20944/preprints201908.0216.v1
Chicago/Turabian Style
Khan, W., Ugur Duran and Mehmet Acikgoz. 2019 "Certain Results on (p,q)-Hermite Based Apostol Type Frobenius-Euler Polynomials" Preprints. https://doi.org/10.20944/preprints201908.0216.v1
Abstract
In the present paper, the (p,q)-Hermite based Apostol type Frobenius-Euler polynomials and numbers are firstly considered and then diverse basic identities and properties for the mentioned polynomials and numbers, including addition theorems, difference equations, integral representations, derivative properties, recurrence relations. Moreover, we provide summation formulas and relations associated with the Stirling numbers of the second kind.
Keywords
Hermite polynomials, Apostol type Frobenius-Euler polynomials, Hermite based Apostol type Frobenius Euler polynomials, Stirling numbers of the second kind, (p,q)-numbers.
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
