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\(q\)-analogues of the Bernoulli and Genocchi polynomials and the Srivastava-Pintér addition theorems. (English) Zbl 1253.11027

Summary: The main purpose of this paper is to introduce and investigate a new class of generalized Bernoulli and Genocchi polynomials based on the \(q\)-integers. The \(q\)-analogues of well-known formulas are derived. The \(q\)-analogue of the Srivastava-Pintér addition theorem is obtained.

MSC:

11B68 Bernoulli and Euler numbers and polynomials
11B65 Binomial coefficients; factorials; \(q\)-identities
05A30 \(q\)-calculus and related topics
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