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On degenerate Apostol-type polynomials and applications

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Abstract

The main object of the current paper is to introduce and investigate a new unified class of the degenerate Apostol-type polynomials. These polynomials are studied by means of the generating function, series definition and are framed within the context of monomiality principle. Several important recurrence relations and explicit representations for the antecedent class of polynomials are derived. As the special cases, the degenerate Apostol–Bernoulli, Euler and Genocchi polynomials are obtained and corresponding results are also proved. A fascinating example is constructed in terms of truncated-exponential polynomials, which gives the applications of these polynomials to produce their hybridized forms.

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Acknowledgements

This work is jointly supported by Senior Research Fellowship [Award letter no. F./2014-15/NFO-2014-15-OBC-UTT-24168/(SA-III/Website)] awarded to Ms. Tabinda Nahid by the University Grants Commission, Government of India, New Delhi and by Post-Doctoral Fellowship (Office Memo no. 2/40(38)/2016/R&D-II/1063) awarded to Dr. Mumtaz Riyasat by the National Board of Higher Mathematics, Department of Atomic Energy, Government of India, Mumbai.

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  1. Department of Mathematics, Aligarh Muslim University, Aligarh, India

    Subuhi Khan, Tabinda Nahid & Mumtaz Riyasat

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  1. Subuhi Khan
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  2. Tabinda Nahid
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  3. Mumtaz Riyasat
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Correspondence to Tabinda Nahid.

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Khan, S., Nahid, T. & Riyasat, M. On degenerate Apostol-type polynomials and applications. Bol. Soc. Mat. Mex. 25, 509–528 (2019). https://doi.org/10.1007/s40590-018-0220-z

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  • DOI: https://doi.org/10.1007/s40590-018-0220-z

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