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Some generalized Lagrange-based Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials

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Abstract

In this paper, we introduce a general family of Lagrange-based Apostol-type polynomials thereby unifying the Lagrange-based Apostol-Bernoulli and the Lagrange-based Apostol-Genocchi polynomials. We also define Lagrange-based Apostol-Euler polynomials via the generating function. In terms of these generalizations, we find new and useful relations between the unified family and the Apostol-Euler polynomials. We also derive their explicit representations and list some basic properties of each of them. Further relations between the above-mentioned polynomials, including a family of bilinear and bilateral generating functions, are given. Moreover, a generating relation involving the Stirling numbers of the second kind is derived.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, V8W 3R4, Canada

    H. M. Srivastava

  2. Department of Mathematics, Faculty of Arts and Sciences, Eastern Mediterranean University Gazimağusa, TR-33310, Mersin, Turkey

    M. A. Özarslan

  3. Department of Mathematics, Faculty of Engineering, Cyprus International University, Lefkoşa, TR-33310, Mersin, Turkey

    C. Kaanoğlu

Authors
  1. H. M. Srivastava
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  2. M. A. Özarslan
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  3. C. Kaanoğlu
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Correspondence to H. M. Srivastava.

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Srivastava, H.M., Özarslan, M.A. & Kaanoğlu, C. Some generalized Lagrange-based Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials. Russ. J. Math. Phys. 20, 110–120 (2013). https://doi.org/10.1134/S106192081301010X

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  • DOI: https://doi.org/10.1134/S106192081301010X

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