Multiple-poly-Bernoulli polynomials of the second kind associated with Hermite polynomials

• Autorzy: Khan W. A. , Ghayasuddin M. , Shadab M.

Identyfikatory

DOI

10.1515/fascmath-2017-0007

• Języki publikacji: EN

Abstrakty

EN

In this paper, we introduce a new class of Hermite multiple-poly-Bernoulli numbers and polynomials of the second kind and investigate some properties for these polynomials. We derive some implicit summation formulae and general symmetry identities by using different analytical means and applying generating functions. The results derived here are a generalization of some known summation formulae earlier studied by Pathan and Khan.

Słowa kluczowe

EN

Hermite polynomials; multi-poly-Bernoulli polynomials of the second kind; Hermite multi-poly-Bernoulli polynomials of the second kind; summation formulae; symmetric identities

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2017
• Tom: Nr 58
• Strony: 97--112
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Khan W. A.

• Department of Mathematics, Faculty of Science, Integral University, Lucknow-226026, India

autor

Ghayasuddin M.

• Department of Mathematics, Faculty of Science, Integral University, Lucknow-226026, India

autor

Shadab M.

• Department of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamiamillia Islamia (A Central University), New Delhi-110025, India

Bibliografia

• [1] Andrews L.C., Special functions for engineers and mathematicians, Macmillan. Co., New York, 1985.
• [2] Arakawa T., Kaneko M., Multiple zeta values, poly-Bernoulli numbers, and related zeta functions, Nagoya Math. J., 153(1999), 189-209.
• [3] Bell E.T., Exponential polynomials, Ann. of Math., 35(1934), 258-277.
• [4] Carlitz L., A note on Bernoulli and Euler polynomials of the second kind, Scripta Math., 25(1961), 323-330.
• [5] Dattoli G., Lorenzutta S., Cesarano C., Finite sums and generalized forms of Bernoulli polynomials, Rendiconti di Mathematica, 19(1999), 385-391.
• [6] Kaneko M., Poly-Bernoulli numbers, J. de Theorie de Nombres, 9(1997), 221-228.
• [7] Khan W.A., A note on Hermite-based poly-Euler and multi poly-Euler polynomials, Palestine J. Math., 5(1)(2016), 17-26.
• [8] Kim T., Kwaon H.I., Lee S.H, Seo J.J., A note on poly-Bernoulli numbers and polynomials of the second kind, Advances in Difference Equations, 219(2014).
• [9] Pathan M.A., Khan W.A., Some implicit summation formulas and symmetric identities for the generalized Hermite-Bernoulli polynomials, Mediterr. J. Math., 12(2015), 679-695.
• [10] Pathan M.A., Khan W.A., Some new classes of generalized Hermite-based Apostol-Euler and Apostol-Genocchi polynomials, Fasciculi Mathematici, 55(2015), 153-170.
• [11] Qi F., Kim D.S., Kim T., Dolgy D.V., Multiple poly-Bernoulli polynomials of the second kind, Advanced Studies in Contemporary Mathematics, 25(2015), 1-7.
• [12] Roman S., The Umbral Calculus, Volume 111 of Pure and Applies Mathematics, Academic Press, Inc, [Harcourt Brace Jovanovich, Publishers], New York, 1984.
• [13] Srivastava H.M., Manocha H.L., A treatise on generating functions, Ellis Horwood Limited. Co., New York, 1984.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).