scholarly journals On the Distribution of the -Euler Polynomials and the -Genocchi Polynomials of Higher Order

2008 ◽  
Vol 2008 (1) ◽  
pp. 723615 ◽  
Author(s):  
Leechae Jang ◽  
Taekyun Kim
Keyword(s):  
Higher Order ◽  
Euler Polynomials ◽  
Genocchi Polynomials

scholarly journals On the unified family of generalized Apostol-type polynomials of higher order and multiple power sums

Filomat ◽  
2016 ◽  
Vol 30 (4) ◽  
pp. 929-935 ◽  
Author(s):  
Veli Kurt
Keyword(s):  
Recurrence Relations ◽  
Higher Order ◽  
Euler Polynomials ◽  
Multiplication Formula ◽  
Power Sums ◽  
Genocchi Polynomials ◽  
Alternating Sums ◽  
Multiple Power

In last last decade, many mathematicians studied the unification of the Bernoulli and Euler polynomials. Firstly Karande B. K. and Thakare N. K. in [6] introduced and generalized the multiplication formula. Ozden et. al. in [14] defined the unified Apostol-Bernoulli, Euler and Genocchi polynomials and proved some relations. M. A. Ozarslan in [13] proved the explicit relations, symmetry identities and multiplication formula. El-Desouky et. al. in ([3], [4]) defined a new unified family of the generalized Apostol-Euler, Apostol-Bernoulli and Apostol-Genocchi polynomials and gave some relations for the unification of multiparameter Apostol-type polynomials and numbers. In this study, we give some symmetry identities and recurrence relations for the unified Apostol-type polynomials related to multiple alternating sums.

scholarly journals Higher-Order Convolutions for Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi Polynomials

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 329 ◽  
Author(s):  
Yuan He ◽  
Serkan Araci ◽  
Hari Srivastava ◽  
Mahmoud Abdel-Aty
Keyword(s):  
Generating Function ◽  
Bernoulli Polynomials ◽  
Higher Order ◽  
Euler Polynomials ◽  
Genocchi Polynomials

In this paper, we present a systematic and unified investigation for the Apostol-Bernoulli polynomials, the Apostol-Euler polynomials and the Apostol-Genocchi polynomials. By applying the generating-function methods and summation-transform techniques, we establish some higher-order convolutions for the Apostol-Bernoulli polynomials, the Apostol-Euler polynomials and the Apostol-Genocchi polynomials. Some results presented here are the corresponding extensions of several known formulas.

scholarly journals A Note on (h,q)-Genocchi Polynomials and Numbers of Higher Order

2010 ◽  
Vol 2010 ◽  
pp. 1-7 ◽  
Author(s):  
Lee-Chae Jang ◽  
Kyung-Won Hwang ◽  
Young-Hee Kim
Keyword(s):  
Higher Order ◽  
Genocchi Polynomials

scholarly journals A note on the higher-order Frobenius-Euler polynomials and Sheffer sequences

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
Dae San Kim ◽  
Taekyun Kim ◽  
Sang-Hun Lee ◽  
Seog-Hoon Rim
Keyword(s):  
Higher Order ◽  
Euler Polynomials ◽  
Sheffer Sequences

On modified higher-order q-Euler polynomials under S_5

2015 ◽  
Vol 9 ◽  
pp. 4171-4178
Author(s):  
Taekyun Kim ◽  
Jong Jin Seo
Keyword(s):  
Higher Order ◽  
Euler Polynomials

scholarly journals Some Identities on the Generalizedq-Bernoulli,q-Euler, andq-Genocchi Polynomials

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Daeyeoul Kim ◽  
Burak Kurt ◽  
Veli Kurt
Keyword(s):  
Recurrence Relations ◽  
Analogous Result ◽  
Bernoulli Polynomials ◽  
Addition Theorem ◽  
Euler Polynomials ◽  
Genocchi Polynomials

Mahmudov (2012, 2013) introduced and investigated someq-extensions of theq-Bernoulli polynomialsℬn,qαx,yof orderα, theq-Euler polynomialsℰn,qαx,yof orderα, and theq-Genocchi polynomials𝒢n,qαx,yof orderα. In this paper, we give some identities forℬn,qαx,y,𝒢n,qαx,y, andℰn,qαx,yand the recurrence relations between these polynomials. This is an analogous result to theq-extension of the Srivastava-Pintér addition theorem in Mahmudov (2013).

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