论文信息 - An invariant p-adic q-integral associated with q-Euler numbers and polynomials

An invariant p-adic q-integral associated with q-Euler numbers and polynomials

Abstract The purpose of this paper is to consider q-Euler numbers and polynomials which are q-extensions of ordinary Euler numbers and polynomials by the computations of the p-adic q-integrals due to T. Kim, cf. [1, 3, 6, 12], and to derive the "complete sums for q-Euler polynomials" which are evaluated by using multivariate p-adic q-integrals. These sums help us to study the relationships between p-adic q-integrals and non-archimedean combinatorial analysis.

S. Rim | Y. Simsek | I. Cangül | V. Kurt | H. Pak

[1] Taekyun Kim,et al. On aq-Analogue of thep-Adic Log Gamma Functions and Related Integrals , 1999 .

[2] Taekyun Kim,et al. An Invariant P -Adic Integral Associated with Daehee Numbers , 2002 .

[3] Taekyun Kim,et al. p-adic q-integrals associated with the Changhee–Barnes' q-Bernoulli polynomials , 2004 .

[4] Sums of powers of consecutive q-integers , 2005, math/0501531.

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

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

[7] On the analogs of Euler numbers and polynomials associated with p-adic integrals on the rings of p-a , 2006, math/0607180.

[8] Taekyun Kim. Multiple p-adic L-function , 2005, math/0505133.

[9] q-Analogue of Euler-Barnes Multiple Zeta Functions (= a note on q-zeta functions) , 2006, math/0603144.

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