A note on generalized Euler numbers and polynomials

In this paper we construct new generalized Euler polynomials and generalized Euler numbers attached to χ. We investigate some of the properties that are related to generalized Euler polynomials. We also derive the existence of a specific interpolation function that interpolates generalized Euler polynomials at negative integers. Finally, we investigate computationally the roots of the generalized Euler polynomials E n, χ(x) for values of the index n.

[1]  Taekyun Kim.  On p-adic q-l-functions and sums of powers , 2007 .

[2]  Elias Deeba,et al.  Stirling's series and Bernoulli numbers , 1991 .

[3]  Ravi P. Agarwal,et al.  Exploring the multiple Changhee q-Bernoulli polynomials , 2005, Int. J. Comput. Math..

[4]  Boris A Kupershmidt.  Reflection Symmetries of q-Bernoulli Polynomials , 2005 .

[5]  Jang Lee Chae,et al.  A study on the distribution of twisted q-Genocchi polynomials , 2009 .

[6]  Taekyun Kim,et al.  On the q-extension of Euler and Genocchi numbers , 2007 .

[7]  Takashi Agoh,et al.  On Bernoulli and Euler numbers , 1988 .

[8]  Hacer Ozden,et al.  A note on p-adic q-Euler measure , 2007 .

[9]  Yilmaz Simsek,et al.  On (i, q) Bernoulli and Euler numbers , 2008, Appl. Math. Lett..

[10]  Yilmaz Simsek,et al.  Remarks on q-Bernoulli numbers associated with Daehee numbers , 2009 .

[11]  Taekyun Kim,et al.  On the analogs of Euler numbers and polynomials associated with p-adic q-integral on Zp at q=−1 , 2007 .

[12]  Yilmaz Simsek,et al.  q-Analogue of twisted l-series and q-twisted Euler numbers , 2005 .

[13]  Taekyun Kim,et al.  Euler Numbers and Polynomials Associated with Zeta Functions , 2008, 0801.0329.

[14]  Yilmaz Simsek,et al.  On p-adic twisted q-L-functions related to generalized twisted Bernoulli numbers , 2006 .

[15]  Taekyun Kim,et al.  On p-adic interpolating function for q-Euler numbers and its derivatives , 2008 .

[16]  T. Kim.  A note on q-Volkenborn integration , 2005 .

[17]  Taekyun Kim.  $q$-Volkenborn Integration and Its Applications , 2005 .

[18]  C. S. Ryoo,et al.  Exploring the q-Riemann zeta function and q-Bernoulli polynomials , 2005 .

[19]  Taekyun Kim.  q-Euler numbers and polynomials associated with p-adic q-integrals , 2007 .

[20]  Katsumi Shiratani,et al.  On a p-adic interpolation function for the Euler numbers and its derivatives , 1985 .