Generalized Apostol Type Polynomials Based on Twin-Basic Numbers

Authors

  • Ugur Duran Department of Basic Sciences of Engineering, Faculty of Engineering and Natural Sciences, Iskenderun Tecnical University, TR-31200 Hatay
  • Mehmet Acikgoz Department of Mathematics, Faculty of Arts and Science, University of Gaziantep, TR-27310 Gaziantep
  • Hemen Dutta Department of Mathematics, Gauhati University, Guwahati 781014, Assam

DOI:

https://doi.org/10.26713/cma.v11i1.1327

Keywords:

\((p, q)\)-calculus, Apostol-Bernoulli polynomials, Apostol-Euler polynomials, Apostol-Genocchi polynomials, Stirling numbers of second kind, Bernstein polynomials, Gamma function, Generating function, Cauchy product

Abstract

In this work, we consider a class of new generating function for \((p,q)\)-analog of Apostol type polynomials of order \(\alpha\) including Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials of order \(\alpha\). By making use of their generating function, we derive some useful identities. We also introduce the generating functions of \((p,q)\)-analogues of the Stirling numbers of second kind of order \(\tau\) and the Bernstein polynomials by which we construct diverse correlations including aforementioned polynomials and the \((p,q)\)-gamma function.

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Published

31-03-2020
CITATION

How to Cite

Duran, U., Acikgoz, M., & Dutta, H. (2020). Generalized Apostol Type Polynomials Based on Twin-Basic Numbers. Communications in Mathematics and Applications, 11(1), 65–83. https://doi.org/10.26713/cma.v11i1.1327

Issue

Vol. 11 No. 1 (2020)

Section

Research Article

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