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Certain new presentation of the generalized polynomials and numbers

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Abstract

In this paper, we propose two new generalizations of the Bernoulli polynomials and numbers by means of the Wiman function. We also consider the variations in the generating functions of our proposed polynomials. Some interesting properties of our generalized polynomials are given in a systematic way. Furthermore, certain new classes of multi-index generalized polynomials and numbers are presented in the last section as the conclusion of our current investigation.

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Acknowledgements

The authors are grateful to the referees for their valuable comments, which improved the quality of the work and the presentation of the paper. Also, the authors would like to thank the Science and Engineering Research Board (SERB), Department of Science and Technology, Government of India for project under the Mathematical Research Impact Centric Support (MATRICES) with reference no. 2017/000821 for this work.

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Authors and Affiliations

  1. Department of Mathematics, Integral University Campus, Shahjahanpur, 242002, India

    Mohd Ghayasuddin

  2. Department of Applied Mathematics, Faculty of Engineering and Technology, Aligarh Muslim University, Aligarh, 202002, India

    Nabiullah Khan

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  1. Mohd Ghayasuddin
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  2. Nabiullah Khan
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Correspondence to Mohd Ghayasuddin.

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Ghayasuddin, M., Khan, N. Certain new presentation of the generalized polynomials and numbers. Rend. Circ. Mat. Palermo, II. Ser 70, 327–339 (2021). https://doi.org/10.1007/s12215-020-00502-9

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  • DOI: https://doi.org/10.1007/s12215-020-00502-9

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