论文信息 - On (i, q) Bernoulli and Euler numbers

On (i, q) Bernoulli and Euler numbers

Abstract The p -adic invariant q -integral on Z p was originally constructed by T. Kim [T. Kim, On a q -analogue of the p -adic log gamma function and related integrals, J. Number Theory 76 (1999) 320–329]. Recently, many authors have been studying the extended Bernoulli numbers or Euler numbers by using this p -adic q -integral in the fermionic or bosonic sense. Let i ∈ O C p = { x ∈ C p : | x | p ⩽ 1 } . Then we consider new ( i , q ) -Bernoulli and Euler numbers using p -adic q -integrals in this work.

Yilmaz Simsek | Mehmet Cenkci | V. Kurt | S. H. Rim

[1] Taekyun Kim. A New approach to q-zeta function , 2005 .

[2] S. Rim,et al. On the twisted q-Euler numbers and polynomials associated with basic q-l-functions , 2006, math/0611807.

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

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

[5] Leonard Carlitz,et al. $q$-Bernoulli and Eulerian numbers , 1954 .

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

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

[8] Yilmaz Simsek,et al. Twisted (h,q)-Bernoulli numbers and polynomials related to twisted (h,q)-zeta function and L-function☆ , 2006 .

[9] Leonard Carlitz,et al. Eulerian Numbers and Polynomials , 1959 .

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

[11] Taekyun Kim,et al. ON EXPLICIT FORMULAS OF p-ADIC q-L-FUNCTIONS , 1994 .

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