# On Genocchi Numbers and Polynomials

## Related Articles

- Zeros of Analytic Continued q-Euler Polynomials and q-Euler Zeta Function. Ryoo, C. S. // Journal of Applied Mathematics;2014, p1
We study that the q-Euler numbers En, q and q-Euler polynomials En, q(x) are analytic continued to Eq(s) and Eq(s,Ï‰).We investigate the new concept of dynamics of the zeros of analytic continued polynomials. Finally, we observe an interesting phenomenon of "scattering" of the zeros of...

- Exploring the q-Euler numbers and polynomials. Kim, T.; Ryoo, C. S. // Journal of Concrete & Applicable Mathematics;Oct2009, Vol. 7 Issue 4, p349
In this paper we observe the structure of the roots of q-Euler polynomials En(x; h|q), using numerical investigation. We study that the q-Euler polynomial are analytic continued to Eq(s). A new formula for the q-Euler Zeta function ?E,q(s|h), in terms of nested series of ?E,q(n|h) is derived.

- On Polynomials Interpolating Between the Stationary State of a O( n) Model and a Q.H.E. Ground State. Kasatani, M.; Pasquier, V. // Communications in Mathematical Physics;Nov2007, Vol. 276 Issue 2, p397
We obtain a family of polynomials defined by vanishing conditions and associated to tangles. We study more specifically the case where they are related to a O( n) loop model. We conjecture that their specializations at z i = 1 are positive in n. At n = 1, they coincide with the...

- A New Method for Polynomial Interpolation. Majdodin, Rooholah; Farhadi, Hamidreza // Enformatika;2007, Vol. 19, p298
In this article we introduce a new approach to polynomial interpolation. The time and space complexity of the algorithm is discussed in the end.

- A FAMILY OF BARNES-TYPE MULTIPLE TWISTED q-EULER NUMBERS AND POLYNOMIALS RELATED TO FERMIONIC p-ADIC INVARIANT INTEGRALS ON â„¤p. Lee-Chae Jang // Journal of Computational Analysis & Applications;Feb2011, Vol. 13 Issue 2, p376
In this paper, by using the fermionic p-adic invariant integrals, we consider the twisted q-extension of the Barnes-type multiple q-Euler polynomials and numbers and discuss some properties of them. In particular, we present a systemic study of the generalized Barnes-type multiple twisted...

- RECOGNIZING SOLUBLE GROUPS FROM THEIR PROBABILISTIC ZETA FUNCTIONS. ELOISA DETOMI; ANDREA LUCCHINI // Bulletin of the London Mathematical Society;Sep2003, Vol. 35 Issue 5, p659
It is proved that if $P_G(s)$ has an Euler product expansion with all factors of the form $1-c_i/q_i^s$ where each $q_i$ is a prime power, then $G$ is soluble.

- A weak form of interpolation in equational logic. Maksimova, L. L. // Algebra & Logic;Jan2008, Vol. 47 Issue 1, p56
The notions of a weak interpolation property and of weak amalgamation are introduced. It is proved that in varieties with the congruence extension property, the weak interpolation property is equivalent to the weak amalgamation property. In turn, weak amalgamability of a variety is equivalent to...

- Weak interpolation in extensions of the logics S 4 and K 4. Karpenko, A. // Algebra & Logic;Nov2008, Vol. 47 Issue 6, p395
Conditions are specified which are necessary and sufficient for a logic over K4 to possess the weak interpolation property. For this goal to be met, simple transitive modal algebras are described, and we establish a criterion for the class of such algebras to be amalgamable. For extensions of...

- Some Relations of the Twisted q-Genocchi Numbers and Polynomials with Weight a and Weak Weight ÃŸ. Kang, J. Y.; Lee, H. Y.; Jung, N. S. // Abstract & Applied Analysis;2012, p1
Recently many mathematicians are working on Genocchi polynomials and Genocchi numbers. We define a new type of twisted q-Genocchi numbers and polynomialswithweight a andweakweight ÃŸ and give some interesting relations of the twisted q-Genocchi numbers and polynomials with weight a and weak...