Mahmudov, N. I. \(q\)-analogues of the Bernoulli and Genocchi polynomials and the Srivastava-Pintér addition theorems. (English) Zbl 1253.11027 Discrete Dyn. Nat. Soc. 2012, Article ID 169348, 8 p. (2012). 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. Cited in 3 ReviewsCited in 10 Documents MSC: 11B68 Bernoulli and Euler numbers and polynomials 11B65 Binomial coefficients; factorials; \(q\)-identities 05A30 \(q\)-calculus and related topics Keywords:generalized Bernoulli polynomials; generalized Genocchi polynomials; \(q\)-integers; \(q\)-analogue of the Srivastava-Pintér addition theorem PDFBibTeX XMLCite \textit{N. I. Mahmudov}, Discrete Dyn. Nat. Soc. 2012, Article ID 169348, 8 p. (2012; Zbl 1253.11027) Full Text: DOI References: [1] 71 (1999) [2] DOI: 10.1215/S0012-7094-48-01588-9 · Zbl 0032.00304 · doi:10.1215/S0012-7094-48-01588-9 [3] DOI: 10.1016/S0893-9659(04)90077-8 · Zbl 1070.33012 · doi:10.1016/S0893-9659(04)90077-8 [4] DOI: 10.1016/j.jmaa.2006.03.037 · Zbl 1112.11012 · doi:10.1016/j.jmaa.2006.03.037 [5] DOI: 10.1155/2007/71452 · Zbl 1188.11005 · doi:10.1155/2007/71452 [6] Advanced Studies in Contemporary Mathematics 17 (1) pp 9– (2008) [7] DOI: 10.4134/JKMS.2006.43.1.183 · Zbl 1129.11008 · doi:10.4134/JKMS.2006.43.1.183 [8] DOI: 10.1155/2008/815750 · Zbl 1140.33308 · doi:10.1155/2008/815750 [9] Transactions of the American Mathematical Society 76 pp 332– (1954) [10] DOI: 10.1016/j.amc.2007.10.033 · Zbl 1146.33001 · doi:10.1016/j.amc.2007.10.033 [11] DOI: 10.1016/j.amc.2009.06.060 · Zbl 1220.11028 · doi:10.1016/j.amc.2009.06.060 [12] Taiwanese Journal of Mathematics 15 (1) pp 241– (2011) [13] (2012) [14] European Journal of Pure and Applied Mathematics 5 (2) pp 97– (2012) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.