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Axioms 2012, 1(3), 395-403; doi:10.3390/axioms1030395
Article
Generating Functions for q-Apostol Type Frobenius–Euler Numbers and Polynomials
Department of Mathematics, Faculty of Arts and Science, University of Akdeniz, 07058 Antalya, Turkey
Received: 30 October 2012; in revised form: 26 November 2012 / Accepted: 28 November 2012 / Published: 7 December 2012
(This article belongs to the Special Issue q-Series and Related Topics in Special Functions and Analytic Number Theory)
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Abstract: The aim of this paper is to construct generating functions, related to nonnegative real parameters, for q-Eulerian type polynomials and numbers (or q-Apostol type Frobenius–Euler polynomials and numbers). We derive some identities for these polynomials and numbers based on the generating functions and functional equations. We also give multiplication formula for the generalized Apostol type Frobenius–Euler polynomials.
Keywords: Euler Numbers; Frobenius–Euler Numbers; Frobenius–Euler polynomials; q-Frobenius–Euler polynomials; q-series; Generating function
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MDPI and ACS Style
Simsek, Y. Generating Functions for q-Apostol Type Frobenius–Euler Numbers and Polynomials. Axioms 2012, 1, 395-403.
AMA StyleSimsek Y. Generating Functions for q-Apostol Type Frobenius–Euler Numbers and Polynomials. Axioms. 2012; 1(3):395-403.
Chicago/Turabian StyleSimsek, Yilmaz. 2012. "Generating Functions for q-Apostol Type Frobenius–Euler Numbers and Polynomials." Axioms 1, no. 3: 395-403.