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Volume 11
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10.3390/sym11040538
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Article

A Note on the Truncated-Exponential Based Apostol-Type Polynomials

by
H. M. Srivastava
1,2,*,
Serkan Araci
3,
Waseem A. Khan
4 and
Mehmet Acikgöz
5
1
Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
2
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
3
Department of Economics, Faculty of Economics, Administrative and Social Science, Hasan Kalyoncu University, TR-27410 Gaziantep, Turkey
4
Department of Mathematics, Integral University, Lucknow 226026, Uttar Pradesh, India
5
Department of Mathematics, Faculty of Science and Arts, Gaziantep University, TR-27310 Gaziantep, Turkey
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(4), 538; https://doi.org/10.3390/sym11040538
Submission received: 3 April 2019 / Revised: 10 April 2019 / Accepted: 12 April 2019 / Published: 15 April 2019
(This article belongs to the Special Issue Integral Transforms and Operational Calculus)
Versions Notes

Abstract

In this paper, we propose to investigate the truncated-exponential-based Apostol-type polynomials and derive their various properties. In particular, we establish the operational correspondence between this new family of polynomials and the familiar Apostol-type polynomials. We also obtain some implicit summation formulas and symmetric identities by using their generating functions. The results, which we have derived here, provide generalizations of the corresponding known formulas including identities involving generalized Hermite-Bernoulli polynomials.
Keywords: truncated-exponential polynomials; monomiality principle; generating functions; Apostol-type polynomials and Apostol-type numbers; Bernoulli, Euler and Genocchi polynomials; Bernoulli, Euler, and Genocchi numbers; operational methods; summation formulas; symmetric identities truncated-exponential polynomials; monomiality principle; generating functions; Apostol-type polynomials and Apostol-type numbers; Bernoulli, Euler and Genocchi polynomials; Bernoulli, Euler, and Genocchi numbers; operational methods; summation formulas; symmetric identities

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MDPI and ACS Style

Srivastava, H.M.; Araci, S.; Khan, W.A.; Acikgöz, M. A Note on the Truncated-Exponential Based Apostol-Type Polynomials. Symmetry 2019, 11, 538. https://doi.org/10.3390/sym11040538

AMA Style

Srivastava HM, Araci S, Khan WA, Acikgöz M. A Note on the Truncated-Exponential Based Apostol-Type Polynomials. Symmetry. 2019; 11(4):538. https://doi.org/10.3390/sym11040538

Chicago/Turabian Style

Srivastava, H. M., Serkan Araci, Waseem A. Khan, and Mehmet Acikgöz. 2019. "A Note on the Truncated-Exponential Based Apostol-Type Polynomials" Symmetry 11, no. 4: 538. https://doi.org/10.3390/sym11040538

APA Style

Srivastava, H. M., Araci, S., Khan, W. A., & Acikgöz, M. (2019). A Note on the Truncated-Exponential Based Apostol-Type Polynomials. Symmetry, 11(4), 538. https://doi.org/10.3390/sym11040538

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