# On the Symmetries of the q-Bernoulli Polynomials

## Related Articles

- Identities on the Bernoulli and Genocchi Numbers and Polynomials. Seog-Hoon Rim; Joohee Jeong; Sun-Jung Lee // International Journal of Mathematics & Mathematical Sciences;2012, p1
We give some interesting identities on the Bernoulli numbers and polynomials, on the Genocchi numbers and polynomials by using symmetric properties of the Bernoulli and Genocchi polynomials.

- CALCULATING ZEROS OF THE SECOND KIND q-BERNOULLI POLYNOMIALS. Ryoo, C. S. // Journal of Computational Analysis & Applications;Jan2012, Vol. 14 Issue 1, p314
In this paper, we observe the behavior of real roots of the second kind q-Bernoulli polynomials Bn,q(x) for 0 < q < 1. By means of numerical experiments, we demonstrated a remarkably regular structure of the complex roots of the second kind q-Bernoulli polynomials Bn,q(x) for -1 < q < 0. The...

- Calculating zeros of q-extension of the second kind Bernoulli polynomials. Ryoo, C. S. // Journal of Computational Analysis & Applications;Feb2013, Vol. 15 Issue 2, p248
In this paper we observe the behavior of complex roots of q-extension of the second kind Bernoulli polynomials Bn,q(x), using numerical investigation. By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of of (q-extension of the second kind...

- SOME IDENTITIES OF THE GENERALIZED TWISTED BERNOULLI NUMBERS AND POLYNOMIALS OF HIGHER ORDER. Seog-Hoon Rim; Young-Hee Kim; Byungje Lee; Taekyun Kim // Journal of Computational Analysis & Applications;Jul2010, Vol. 12 Issue 3, p695
The purpose of this paper is to derive some identities of the higher order generalized twisted Bernoulli numbers and polynomials attached to x from the properties of the p-adic invariant integral. We give some interesting identities for the power sums and the generalized twisted Bernoulli...

- Some Identities of Symmetry for the Generalized Bernoulli Numbers and Polynomials. Taekyun Kim; Seog-Hoon Rim; Byungje Lee // Abstract & Applied Analysis;2009, Special section p1
By the properties of p-adic invariant integral on Zp, we establish various identities concerning the generalized Bernoulli numbers and polynomials. From the symmetric properties of p-adic invariant integral on Zp, we give some interesting relationship between the power sums and the generalized...

- A note on degenerate poly-Bernoulli numbers and polynomials. Kim, Dae; Kim, Taekyun // Advances in Difference Equations;8/1/2015, Vol. 2015 Issue 1, p1
In this paper, we consider the degenerate poly-Bernoulli polynomials and present new and explicit formulas for computing them in terms of the degenerate Bernoulli polynomials and Stirling numbers of the second kind.

- On $(h,q)$-Daehee numbers and polynomials. Do, Younghae; Lim, Dongkyu // Advances in Difference Equations;9/15/2015, Vol. 2015 Issue 1, p1
The p-adic q-integral (sometimes called q-Volkenborn integration) was defined by Kim. From p-adic q-integral equations, we can derive various q-extensions of Bernoulli polynomials and numbers. DS Kim and T Kim studied Daehee polynomials and numbers and their applications. Kim et al. introduced...

- A Note on Symmetric Properties of the Twisted í‘ž-Bernoulli Polynomials and the Twisted Generalized í‘ž-Bernoulli Polynomials. Jang, L.-C.; Yi, H.; Shivashankara, K.; Kim, T.; Kim, Y. H.; Lee, B. // Advances in Difference Equations;2010, Special section p1
No abstract available.

- SOME IDENTITIES ON THE EXTENDED CARLITZ'S q-BERNOULLI NUMBERS AND POLYNOMIALS. Seog-Hoon Rim; Tae-Kyun Kim; Byung-Je Lee // Journal of Computational Analysis & Applications;Apr2012, Vol. 14 Issue 3, p536
In Kim introduced the p-adic q-integral on â„¤p (= q-Volkenborn integral) and gave some Witt's formula for the Carlitz's q-Bernoulli numbers and polynomials. In this paper we investigate some properties of the extended Carlitz's q-Bernoulli numbers and polynomials by using p-adic q-integral...