A note on q-truncated exponential polynomials

Authors

  • N. Raza Aligarh Muslim University, Aligarh 202002, India
  • M. Fadel Aligarh Muslim University, Aligarh 202002, India; University of Lahej, 73560 Lahej, Yemen https://orcid.org/0000-0002-6206-9113
  • C. Cesarano International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Rome, Italy
https://doi.org/10.15330/cmp.16.1.128-147

Keywords:

quantum calculus, truncated exponential polynomials, recurrence relations, summation and integral formulas, q-Hermite polynomials, q-dilatation operator
Published online: 2024-05-27

Abstract

In this paper, we introduce the q-truncated exponential polynomials by means of the integral form. Certain properties of the q-truncated exponential polynomials like series definition, recurrence relations, q-differential equations and integral representations are obtained. Also, we introduce the associated q-truncated exponential polynomials, higher order q-truncated exponential polynomials and higher order associated q-truncated exponential polynomials. Furthermore, we obtain their integral forms, generating functions, series definitions, summation and operational formulas.

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How to Cite
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Raza, N.; Fadel, M.; Cesarano, C. A Note on q-Truncated Exponential Polynomials. Carpathian Math. Publ. 2024, 16, 128-147.