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Search Results: 1 - 10 of 7342 matches for " Genocchi polynomials of higher order "
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Normalized polynomials and their multiplication formulas
Rahime Dere and Yilmaz Simsek
Advances in Difference Equations , 2013, DOI: 10.1186/1687-1847-2013-31
Abstract: AMS Subject Classification: 05A40, 11B83, 11B68.
New Extension of Unified Family Apostol-Type of Polynomials and Numbers  [PDF]
Beih El-Sayed El-Desouky, Rabab Sabry Gomaa
Applied Mathematics (AM) , 2015, DOI: 10.4236/am.2015.69134
Abstract: The purpose of this paper is to introduce and investigate new unification of unified family of Apostol-type polynomials and numbers based on results given in [1] [2]. Also, we derive some properties for these polynomials and obtain some relationships between the Jacobi polynomials, Laguerre polynomials, Hermite polynomials, Stirling numbers and some other types of generalized polynomials.
Multiparameter Higher Order Daehee and Bernoulli Numbers and Polynomials  [PDF]
Beih S. El-Desouky, Abdelfattah Mustafa, Fatma M. Abdel-Moneim
Applied Mathematics (AM) , 2017, DOI: 10.4236/am.2017.86060
Abstract: This paper gives a new generalization of higher order Daehee and Bernoulli numbers and polynomials. We define the multiparameter higher order Daehee numbers and polynomials of the first and second kind. Moreover, we derive some new results for these numbers and polynomials. The relations between these numbers and Stirling and Bernoulli numbers are obtained. Furthermore, some interesting special cases of the generalized higher order Daehee and Bernoulli numbers and polynomials are deduced.
Symmetric properties of Genocchi polynomials with weak weight alpha
J. Y. Kang,C. S. Ryoo
Applied Mathematical Sciences , 2013,
Abstract: The main purpose of this paper is to study an identity of symmetryfor the Genocchi polynomials with weak weight α. The Genocchi numbersand polynomials with weak weight α is investigated by C.S.Ryoo,J. Y. Kang [A note on the q-Genocchi numbers and polynomials withweak weight alpha, Applied Mathematical Sciences, Vol. 6, 2012, no.15, 731 - 738]. In this paper, by using this symmetry of fermionic padicq-integral on Zp, we give some interesting relations of symmetrybetween the power sum and Genocchi polynomials with weak weight α.
On the multiple sums of Bernoulli, Euler and Genocchi polynomials
B. Kurt
International Journal of Mathematical Analysis , 2013,
Abstract: We introduce and investigate the Apostol-Bernoulli, Apostol-Eulerand Apostol-Genocchi polynomials by means of a suitable theirs generatingpolynomials. We establish several interesting properties of thesepolynomials. Also, we gave some propositions two theorems and onecorollary.
Unified representation of the family of L-functions
Hacer Ozden and Yilmaz Simsek
Journal of Inequalities and Applications , 2013, DOI: 10.1186/1029-242X-2013-64
Abstract: AMS Subject Classification: 11B68, 11S40, 11S80, 26C05, 30B40.
The degree and the order of polynomials in the ring R [F1A]
Ronnason Chinram
Songklanakarin Journal of Science and Technology , 2007,
Abstract: In this research, we generalize some properties of the degree and the order of polynomials in the ring R[x].
A Fundamental Relationship of Polynomials and Its Proof  [PDF]
Serdar Beji
Advances in Pure Mathematics (APM) , 2018, DOI: 10.4236/apm.2018.86033
Abstract: A fundamental algebraic relationship for a general polynomial of degree n is given and proven by mathematical induction. The stated relationship is based on the well-known property of polynomials that the nth-differences of the subsequent values of an nth-order polynomial are constant.
Higher Education—Educating for Higher Order Skills  [PDF]
Rachel Or-Bach
Creative Education (CE) , 2013, DOI: 10.4236/ce.2013.47A2004

Preparing college students for a knowledge-based economy is a challenge that requires curriculum design that puts more emphasis on learning skills than on content to be taught. Cognitive skills should be practiced in a context of some content, but the choice of content, the choice of the learning environment, and the choice of the assessment procedures can enhance the development of such skills. In this paper we present these choices for a course that was specially designed to provide a motivating and engaging context that requires the use of higher order cognitive skills. The title of the course is “Design of computer-based games and interactive stories” and it is provided to students with no prior exposure to computer programming. At the end of the course students are required to submit an interactive artifact (a game or a story) implemented in Scratch, which is a visual programming environment. In this qualitative study we present the results from a thematic analysis of students’ post-course reflection reports.

Adomian Decomposition Method with Green’s Function for Solving Tenth-Order Boundary Value Problems  [PDF]
Waleed Al-Hayani
Applied Mathematics (AM) , 2014, DOI: 10.4236/am.2014.510136

In this paper, the Adomian decomposition method with Green’s function (Standard Adomian and Modified Technique) is applied to solve linear and nonlinear tenth-order boundary value problems with boundary conditions defined at any order derivatives. The numerical results obtained with a small amount of computation are compared with the exact solutions to show the efficiency of the method. The results show that the decomposition method is of high accuracy, more convenient and efficient for solving high-order boundary value problems.

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