A note on Hermite-based truncated Euler polynomials

  • Waseem A. Khan Prince Mohammad Bin Fahd University
  • Divesh Srivastava Integral University
  • Rifaqat Ali King Khalid University

Résumé

In this paper, we introduce a new class of truncated Hermite-Euler polynomials and numbers as a generalization of Hermite-Euler polynomials. Furthermore, the discussion is on properties and relations with the hypergeometric Bernoulli polynomials, Frobenius-Euler polynomials and Stirling numbers of the second kind. As a result, we derive some implicit summation formulas of this polynomials.

Téléchargements

Les données sur le téléchargement ne sont pas encore disponible.

Biographie de l'auteur

Waseem A. Khan, Prince Mohammad Bin Fahd University

Waseem A. Khan, Research Assistant, Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, P.O Box 1664, Al Khobar

E-mail address: wkhan1@pmu.edu.sa, waseem08 khan@rediffmail.com

Références

Araci, S, Acikgoz, M, em A note on the Frobenius-Euler numbers and polynomials associated with Bernstein polynomials, Adv. Stud. Contemp. Math. 22(3), 399-406 (2012)

Bell, E. T, Exponential polynomials, Ann. of Math., 35, 258-277, (1934). https://doi.org/10.2307/1968431 DOI: https://doi.org/10.2307/1968431

Choi, J, Kim, D. S, Kim, T and Kim, Y. H, A note on some identities of Frobenius-Euler numbers and polynomials, Inter. J. Math. Math. Sci., 2012, 1-9, (2012). https://doi.org/10.1155/2012/861797 DOI: https://doi.org/10.1155/2012/861797

Dattoli, G, Lorenzutta, S and Cesarano, C., Finite sums and generalized forms of Bernoulli polynomials, Rendiconti di Mathematica, 19, 385-391, (1999).

Duran, U, Acikgoz, M and Araci, S, Hermite-based poly-Bernoulli polynomials with a q-paramenter, Adv. Stud. Contemp. Math. (Kyungshang), 28(2), 285-296, (2018). https://doi.org/10.20944/preprints201802.0145.v1 DOI: https://doi.org/10.20944/preprints201802.0145.v1

Duran, U and Acikgoz, M, Truncated Fubini Polynomials, Mathematics, 7, 431, (2019). https://doi.org/10.3390/math7050431 DOI: https://doi.org/10.3390/math7050431

Duran, U and Acikgoz, M, On Degenerate Truncated special polynomials, Mathematics, 8, 144, (2020). https://doi.org/10.3390/math8010144 DOI: https://doi.org/10.3390/math8010144

Hassen, A and Nguyen, H. D, Hypergeometric Bernoulli polynomials and Appell sequences, Int. J. Number Theory, 4, 767-774, (2008). https://doi.org/10.1142/S1793042108001754 DOI: https://doi.org/10.1142/S1793042108001754

Hassen, A and Nguyen, H. D, Hypergeometric zeta functions, Int. J. Number Theory, 6, 99-126, (2010). https://doi.org/10.1142/S179304211000282X DOI: https://doi.org/10.1142/S179304211000282X

Jang, L. C, Kim, D. S, Jang, G. -W and Kwon, J, Some identities for q-Bernoulli numbers and polynomials arising form q-Bernstein polynomials, Adv. Stud. Contemp. Math. (Kyungshang), 28(4), 659-667, (2018).

Jang, G. W and Kim, T, A note on type 2 degenerate Euler and Bernoulli polynomials, Adv. Stud. Contemp. Math. (Kyungshang), 29(1), 147-159, (2019).

Kamano, K, Sums of products of hypergeometric Bernoulli numbers, J. Number Theory, 130, 2259-2271, (2010). https://doi.org/10.1016/j.jnt.2010.04.005 DOI: https://doi.org/10.1016/j.jnt.2010.04.005

Komatsu, K and Ruiz C. P, Truncated Euler polynomials, Mathematica Slovaca, 68(3), 527-536, (2018). https://doi.org/10.1515/ms-2017-0122 DOI: https://doi.org/10.1515/ms-2017-0122

Kim, D. S and Kim, T, Some identities of Frobenius-Euler polynomials arising from umbral calculus, Adv. Difference Equ., 2012, Article number: 196(2012). https://doi.org/10.1186/1687-1847-2012-196 DOI: https://doi.org/10.1186/1687-1847-2012-196

Kim, D. S, Kim, T, Rim, S. H and Dolgy, D. V, Barne's multiple BErnoulli and Hermite mixed-type polynomials, Proc. Jangjeon Math. Soc., 18(1), 7-19, (2015).

Khan, W. A, Some properties of the generalized Apostol type Hermite-Based polynomials, Kyungpook Math. J., 55, 597-614, (2015). https://doi.org/10.5666/KMJ.2015.55.3.597 DOI: https://doi.org/10.5666/KMJ.2015.55.3.597

Khan, W. A and Ahmad, M, Partially degenerate poly-Bernoulli polynomials associated with Hermite polynomials, Adv. Stud. Contemp. Math. (Kyungshang), 28(3), 487-496, (2018).

Khan, W. A, A new class of heigher-order hypergeometric Bernoulli polynomials associated with Hermite polynomials, Bol. Soc. Paran. Mat., Accepted (2020).

Kim, D. S and Kim, T, Some new identities of Frobenius-Euler numbers and polynomials, J. Ineq. Appl., 2012, 1-10, (2012). https://doi.org/10.1155/2012/619197 DOI: https://doi.org/10.1155/2012/619197

Kim, T, Kwon, H. -I and Jang, G. W, Symmetric identities of heigher-order of degenerate q-Bernoulli polynomials, Adv. Stud. Contemp. Math. (Kyungshang), 27(1), 31-41, (2017).

Kumam, W, Srivastava, H. M and Kumam, P, Truncated-exponential-based Frobenius-Euler polynomials, Advan. Diff. Eq., 2019:530, (2019). https://doi.org/10.1186/s13662-019-2462-0 DOI: https://doi.org/10.1186/s13662-019-2462-0

Kurt, B and Simsek, Y, On the generalized Apostol type Frobenius Euler polynomials, Advances in Differences equations, (2013), 1-9, (2013). https://doi.org/10.1186/1687-1847-2013-1 DOI: https://doi.org/10.1186/1687-1847-2013-1

Pathan, M. A and Khan, W. A, Some implicit summation formulas and symmetric identities for the generalized Hermite-Euler polynomials, East-West J. Maths., 16(1), 92-109, (2014).

Srivastava, H. M, Araci, S, Khan, W. A and Acikgoz, M, A note on the truncated-exponential based Apostol-type polynomials, Symmetry 11, Article ID 538,doi:10.3390/sym11040538, (2019). https://doi.org/10.3390/sym11040538 DOI: https://doi.org/10.3390/sym11040538

Srivastava, H. M and Acikgoz, M, A new approach to Legendre-truncated-exponential-based Sheffer sequences via Riordan arrays, Applied Mathematics and Computation 369, 124683, (2020). https://doi.org/10.1016/j.amc.2019.124683 DOI: https://doi.org/10.1016/j.amc.2019.124683

Srivastava, H. M and Manocha, H. L, A treatise on generating functions, Ellis Horwood Limited, New York, 1984.

Simsek, Y, Generating functions for generalized Striling type numbers, Array type polynomials, Eulerian type polynomials and their applications, Fixed Point Th. Appl., DOI: 1186/1687-1812-2013-87, (2013). https://doi.org/10.1186/1687-1812-2013-87 DOI: https://doi.org/10.1186/1687-1812-2013-87

Publiée
2022-12-21
Rubrique
Articles