Generalized Apostol Type Polynomials Based on Twin-Basic Numbers

Ugur Duran, Mehmet Acikgoz, Hemen Dutta

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.

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

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References


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DOI: http://dx.doi.org/10.26713%2Fcma.v11i1.1327

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