A Unification of the Generalized Multiparameter Apostol-type Bernoulli, Euler, Fubini, and Genocchi Polynomials of Higher Order

被引:5
作者
Acala, Nestor G. [1 ]
机构
[1] Mindanao State Univ, Coll Nat Sci & Math, Math Dept, Marawi City, Lanao Del Sur, Philippines
来源
EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS | 2020年 / 13卷 / 03期
关键词
Fubini polynomials; Bernoulli polynomials; Euler polynomials; Genocchi polynomials; Apostol-type polynomials; Ordered Bell polynomials; Gauss hypergeometric function; Generalized Bernoulli polynomials; Generalized Euler polynomials; Generalized Genocchi polynomials; Generalized Fubini polynomials; UNIFIED PRESENTATION; FAMILIES; IDENTITIES;
D O I
10.29020/nybg.ejpam.v13i3.3757
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Most unifications of the classical or generalized Bernoulli, Euler, and Genocchi polynomials involve unifying any two or all of the three special types of polynomials (see, [1, 4, 9, 18, 19, 21, 24-26, 30, 31]). In this paper, we introduce a new class of multiparameter Fubini-type generalized polynomials that unifies four families of higher order generalized Apostol-type polynomials such as the Apostol-Bernoulli, Apostol-Euler, Apostol-Genocchi, and Apostol-Fubini polynomials. Moreover, we obtain an explicit formula of these unified generalized polynomials in terms of the Gaussian hypergeometric function, and establish several symmetry identities.
引用
收藏
页码:587 / 607
页数:21
相关论文
共 33 条
[1]  
[Anonymous], 2009, APPL MATH SCI
[2]  
[Anonymous], 2005, INT J MATH MATH SCI
[3]  
[Anonymous], 2002, INT J MATH EDUC SCI, DOI DOI 10.1080/002073902760047913
[4]   A new generalization of Apostol type Hermite-Genocchi polynomials and its applications [J].
Araci, Serkan ;
Khan, Waseem A. ;
Acikgoz, Mehmet ;
Ozel, Cenap ;
Kumam, Poom .
SPRINGERPLUS, 2016, 5
[5]  
Corcino R., 2015, Jour. Clas. Anal., V6, P119
[6]   Hermite base Bernoulli type polynomials on the umbral algebra [J].
Dere, R. ;
Simsek, Y. .
RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS, 2015, 22 (01) :1-5
[7]   A unified presentation of three families of generalized Apostol type polynomials based upon the theory of the umbral calculus and the umbral algebra [J].
Dere, Rahime ;
Simsek, Yilmaz ;
Srivastava, H. M. .
JOURNAL OF NUMBER THEORY, 2013, 133 (10) :3245-3263
[8]  
Jang Gwan-Woo, 2017, Advanced Studies in Contemporary Mathematics, V27, P385, DOI 10.17777/ascm2017.27.3.385
[9]  
Jolany H, 2013, B MALAYS MATH SCI SO, V36, P465
[10]  
KARANDE BK, 1975, INDIAN J PURE APPL M, V6, P98