Some (p, q)-analogues of Apostol type numbers and polynomials
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KünyeAcikgoz, M., Araci, S., Duran, U. (2019). Some (P, q)-analogues of apostol type numbers and polynomials. Acta et Commentationes Universitatis Tartuensis de Mathematica, 23(1), 37-50. https://doi.org/10.12697/ACUTM.2019.23.04
We consider a new class of generating functions of the generalizations of Bernoulli and Euler polynomials in terms of (p, q)-integers. By making use of these generating functions, we derive (p, q)-generalizations of several old and new identities concerning Apostol-Bernoulli and Apostol-Euler polynomials. Finally, we define the (p, q)-generalization of Stirling polynomials of the second kind of order v, and provide a link between the (p, q)-generalization of Bernoulli polynomials of order v and the (p, q)-generalization of Stirling polynomials of the second kind of order v.