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A General Class of the Three-Variable Unified Apostol-Type q-Polynomials and Multiple Power q-Sums

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Abstract

The main purpose of this article is to introduce a general class of the three-variable unified Apostol-type q-polynomials and to investigate their properties and characteristics. In particular, the generating function, series expression, and several explicit and recurrence relations for these polynomials are established. The three-variable general Apostol–Bernoulli, Apostol–Euler, and Apostol–Genocchi q-polynomials are studied as special members of this class and the corresponding results for these q-polynomials are also obtained. Some symmetry identities involving multiple power q-sums are established. The particular cases of these identities are also deduced. This article presents the first attempt in the direction of establishing symmetry identities for the generalized class of q-polynomials.

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Authors and Affiliations

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

    Hari Mohan Srivastava

  2. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan, Republic of China

    Hari Mohan Srivastava

  3. Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, Uttar Pradesh, India

    Subuhi Khan & Mumtaz Riyasat

  4. Department of Economics, Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu University, 27410, Gaziantep, Turkey

    Serkan Araci

  5. Department of Mathematics, Faculty of Arts and Science, University of Gaziantep, 27310, Gaziantep, Turkey

    Mehmet Acikgoz

Authors
  1. Hari Mohan Srivastava
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  2. Subuhi Khan
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  3. Serkan Araci
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  4. Mehmet Acikgoz
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  5. Mumtaz Riyasat
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All authors have contributed equally to the writing of this paper.

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Correspondence to Serkan Araci.

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Communicated by Ali Abkar.

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Srivastava, H.M., Khan, S., Araci, S. et al. A General Class of the Three-Variable Unified Apostol-Type q-Polynomials and Multiple Power q-Sums. Bull. Iran. Math. Soc. 46, 519–542 (2020). https://doi.org/10.1007/s41980-019-00273-9

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  • DOI: https://doi.org/10.1007/s41980-019-00273-9

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