Degenerate Hermite poly-Bernoulli numbers and polynomials with q-parameter
DOI:
https://doi.org/10.24193/subbmath.2020.1.01Keywords:
Hermite polynomials, degenerate q-poly-Bernoulli polynomi- als, degenerate Hermite q-poly-Bernoulli polynomials, Summation formulae, Symmetric identities.Abstract
In this paper, we introduce a new class of degenerate Hermite
poly-Bernoulli polynomials with q-parameter and give some identities
of these polynomials related to the Stirling numbers of the second kind.
Some implicit summation formulae and general symmetry identities are
derived by using dierent analytical means and applying generating
functions. These results extend some known summations and identities
of degenerate Hermite poly-Bernoulli numbers and polynomials.
References
Andrews, L. C, Special functions for engineers and mathematicians, Macmillan
Co. New York, 1985.
Bayad, A, Hamahata, Y, Multiple-Polylogarithms and multi-poly-Bernoulli
polynomials, Funct. Approx. Comment. Math., 46,45(2012), 45-61.
Bell, E. T, Exponential polynomials, Ann. of Math., 35(1934), 258-277.
Carlitz, L, Degenerate Stirling Bernoulli and Eulerian numbers, Util. Math.,
(1979), 51-88.
Cesarano, C, Cennamo, G. M, Placidi, L, Humbert polynomials and functions
in terms of Hermite polynomials towards applications to wave propagation,
WSEAS Transactions on Mathematics, 13(2014), 595-602.
Cenkcia, M, Komatsu, T, poly-Bernoulli numbers and polynomials with a q-
parameter, Journal of Number Theory, 152(2015), 38-54.
Dattoli, G, Lorenzutta, S and Cesarano, C, Finite sums and generalized forms
of Bernoulli polynomials, Rendiconti di Mathematica, 19(1999), 385-391.
Degenerate Hermite poly-Bernoulli numbers and polynomials with q-paramet1e3r
Dattoli, G, Lorenzutta, S, Ricci, P. E, Cesarano, C, On a family of hybrid
polynomials, Integral Trasforms and Special Functions, 15(6)(2004), 485-490.
Dattoli, G, Srivastava, H. M, Cesarano, C, The Laguerre and Legendre poly-
nomials from an operational point of view, Applied Mathematics and Compu-
tation, 124(1), (2001), 117-127.
Jung, N. S, Ryoo, C. S, Symmetric identities for degenerate q-poly-Bernoulli
numbers and polynomials, J. Appl. Math. & Informatics, 36(2018), 29-38.
Jolany, H, Mohebbi, H, Some results on generalized multi-poly Bernoulli and
Euler polynomials, Int. J. Math. Comb., 2 (2011), 117-129.
Kaneko, M, Poly-Bernoulli numbers, J. de Theorie de Nombres, 9(1997), 221-
Kim, D. S and Kim, T, A note on degenerate poly-Bernoulli numbers and
polynomials, Advanc. Di. Equat., DOI 10.1186/s13662-015-0595-3, (2015).
Kim, D. S, Dolgy, T and Komatsu, D. V, Barnes type degenerate Bernoulli
polynomials, Adv. Stud. Contemp. Math., 25(1), (2015), 121-146.
Ryoo, C. S, On degenerate q-tangent polynomials of higher order, J. Appl.
Math. & Informatics, 35(2017), 113-120.
Srivastava, H. M and Manocha, H. L, A treatise on generating functions Ellis
Horwood Limited, New York, 1984.
Young, P. T, Degenerate Bernoulli polynomials generalized factorials sums and
their application, J. Number Theory, 128(4)(2008), 738-758.
Downloads
Additional Files
Published
Issue
Section
