On the 𝑞-Euler Numbers and Polynomials with Weight 0 [PDF]
Abstract and Applied Analysis, 2012 The purpose of this paper is to investigate some properties of 𝑞-Euler numbers and polynomials with weight 0. From those 𝑞-Euler numbers with weight 0, we derive some identities on the 𝑞-Euler numbers and polynomials with weight 0.
T. Kim, J. Choi
doaj +5 more sources
Generalizations of Euler numbers and polynomials [PDF]
International Journal of Mathematics and Mathematical Sciences, 2003 The concepts of Euler numbers and Euler polynomials are generalized and some basic properties are investigated.
Qiu-Ming Luo, Feng Qi, Lokenath Debnath
doaj +4 more sources
Explicit Formulas Involving -Euler Numbers and Polynomials [PDF]
Abstract and Applied Analysis, 2012 We deal with -Euler numbers and -Bernoulli numbers. We derive some interesting relations for -Euler numbers and polynomials by using their generating function and derivative operator.
Serkan Araci +2 more
doaj +6 more sources
Relationships between generalized Bernoulli numbers and polynomials and generalized Euler numbers and polynomials. [PDF]
, 2002 Let \(a,b,c\) be positive numbers. The generalized Bernoulli and Euler numbers are defined via the generating functions \(\frac{t}{b^t-a^t}\) and \(\frac{2c^t}{b^{2t}+a^{2t}}\) respectively, so that the classical sequences are obtained if \(a=1\), \(b=c=e\). A generalization of the Bernoulli and Euler polynomials is introduced in a similar way.
Luo, Qiu-Ming, Qi, Feng
core +8 more sources
On generalized Lucas polynomials and Euler numbers [PDF]
Miskolc Mathematical Notes, 2010 In this paper we study the relationship between the generalized Lucas polynomials and the Euler numbers and give several interesting identities involving them.
Nalli, Ayse, Zhang, Tianping
openaire +4 more sources
Generalized -Euler Numbers and Polynomials Associated with -Adic -Integral on [PDF]
International Journal of Mathematics and Mathematical Sciences, 2012 We generalize the Euler numbers and polynomials by the generalized -Euler numbers and polynomials . We observe an interesting phenomenon of “scattering” of the zeros of the generalized -Euler polynomials in complex plane.
H. Y. Lee +3 more
doaj +2 more sources
On the q‐Extension of Apostol‐Euler Numbers and Polynomials [PDF]
Abstract and Applied Analysis, 2008 Recently, Choi et al. (2008) have studied the q‐extensions of the Apostol‐Bernoulli and the Apostol‐Euler polynomials of order n and multiple Hurwitz zeta function. In this paper, we define Apostol′s type q‐Euler numbers En,q,ξ and q‐Euler polynomials En,q,ξ(x). We obtain the generating functions of En,q,ξ and En,q,ξ(x), respectively.
Kim, Young-Hee +2 more
openaire +6 more sources
New Biparametric Families of Apostol-Frobenius-Euler Polynomials level-m [PDF]
Математичні Студії, 2021 We introduce two biparametric families of Apostol-Frobenius-Euler polynomials of level-$m$. We give some algebraic properties, as well as some other identities which connect these polynomial class with the generalized $\lambda$-Stirling type numbers of ...
D. Bedoya +3 more
doaj +2 more sources
Some Properties on the q‐Euler Numbers and Polynomials [PDF]
Abstract and Applied Analysis, 2012 We give some new identities on q‐Euler numbers and polynomials by using the fermionic p‐adic integral on ℤp.
Kim, T., Lee, S.-H.
openaire +5 more sources
A Research on a Certain Family of Numbers and Polynomials Related to Stirling Numbers, Central Factorial Numbers, and Euler Numbers [PDF]
Journal of Applied Mathematics, 2013 Recently, many mathematicians have studied different kinds of the Euler, Bernoulli, and Genocchi numbers and polynomials. In this paper, we give another definition of polynomials Ũn(x).
J. Y. Kang, C. S. Ryoo
doaj +2 more sources