Notes on generalization of the Bernoulli type polynomials |
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Authors: | Burak Kurt Yilmaz Simsek |
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Institution: | Department of Mathematics, Faculty of Science, University of Akdeniz, TR-07058 Antalya, Turkey |
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Abstract: | Recently, Srivastava et al. introduced a new generalization of the Bernoulli, Euler and Genocchi polynomials (see H.M. Srivastava, M. Garg, S. Choudhary, Russian J. Math. Phys. 17 (2010) 251-261] and H.M. Srivastava, M. Garg, S. Choudhary, Taiwanese J. Math. 15 (2011) 283-305]). They established several interesting properties of these general polynomials, the generalized Hurwitz-Lerch zeta functions and also in series involving the familiar Gaussian hypergeometric function. By the same motivation of Srivastava’s et al. 11] and 12], we introduce and derive multiplication formula and some identities related to the generalized Bernoulli type polynomials of higher order associated with positive real parameters a, b and c. We also establish multiple alternating sums in terms of these polynomials. Moreover, by differentiating the generating function of these polynomials, we give a interpolation function of these polynomials. |
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Keywords: | Bernoulli numbers and polynomials Euler polynomials Apostol-Bernoulli polynomials Apostol-Bernoulli polynomials of order α Apostol-Euler polynomials Consecutive sums Generating function Hurwitz-Lerch zeta functions |
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