A NEW CLASS OF GENERALIZED POLYNOMIALS ASSOCIATED WITH HERMITE AND POLY-BERNOULLI POLYNOMIALS

被引:4
作者
Pathan, M. A. [1 ]
Khan, Waseem A. [2 ]
机构
[1] KFRI, Ctr Math & Stat Sci CMSS, Peechi PO, Trichur 680653, Kerala, India
[2] Prince Mohammad Bin Fahd Univ, Dept Math & Nat Sci, POB 1664, Al Khobar 31952, Saudi Arabia
关键词
Hermite polynomials; Bernoulli polynomials; poly-Bernoulli polynomials; Hermitepoly-Bernoulli polynomials; summation formulae; symmetric identities;
D O I
10.18514/MMN.2021.1684
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, we introduce a new class of generalized polynomials associated with the modified Milne-Thomson's polynomials Phi((alpha))(n) (x, nu) of degree n and order alpha introduced by Dere and Simsek. The concepts of poly-Bernoulli numbers, poly-Bernoulli polynomials, Hermite-Bernoulli polynomials and generalized Hermite-Bernoulli polynomials are generalized to polynomials of three positive real parameters. Numerous properties of these polynomials and some relations are established. Some implicit summation formulae and general symmetry identities are derived by using different analytical means and applying generating functions. These results extend some known summations and identities of generalized poly-Bernoulli numbers and polynomials.
引用
收藏
页码:317 / 330
页数:14
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