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Zbl 1238.05025
Luo, Qiu-Ming; Srivastava, H.M.
$q$-extensions of some relationships between the Bernoulli and Euler polynomials. (English)
[J] Taiwanese J. Math. 15, No. 1, 241-257 (2011). ISSN 1027-5487

Summary: The main object of this paper is to give $q$-extensions of several explicit relationships of {\it H. M. Srivastava} and {\it A. Pintér} [Appl. Math. Lett. 17, No. 4, 375--380 (2004; Zbl 1070.33012)] between the Bernoulii and Euler polynomials. We also derive several other formulas in series of Carlitz's $q$-Stirling numbers of the second kind.

MSC 2000:: *11B68 Bernoulli numbers, etc.
11B73 Bell and Stirling numbers
11S80 Other analytic theory of local fields
05A30 q-calculus and related topics

Keywords: Bernoulli polynomials; Euler polynomials; $q$-Bernoulli polynomials; $q$-Euler polynomials; $q$-Bemoulli numbers; $q$-Euler numbers; Kronecker symbol; difference equations; addition theorems; recurrence relationships; $q$-Stirling numbers of the second kind; $q$-extensions

Citations: Zbl 1070.33012

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