## 10 Citations

Identities of Symmetry for q-Euler Polynomials

- Mathematics
- 2010

In this paper, we derive eight basic identities of symmetry in three variables related to q-Euler polynomials and the q -analogue of alternating power sums. These and most of their corollaries are…

Identities of Symmetry for q-Euler Polynomials

- Mathematics
- 2011

In this paper, we derive eight basic identities of symmetry in three variables related to q-Euler polynomials and the q -analogue of alternating power sums. These and most of their corollaries are…

IDENTITIES OF SYMMETRY FOR THE HIGHER ORDER q-BERNOULLI POLYNOMIALS

- Mathematics
- 2014

The study of the identities of symmetry for the Bernoulli polynomials arises from the study of Gauss's multiplication formula for the gamma function. There are many works in this direction. In the…

IDENTITIES OF SYMMETRY FOR GENERALIZED TWISTED BERNOULLI POLYNOMIALS TWISTED BY RAMIFIED ROOTS OF UNITY

- Mathematics
- 2010

Abstract We derive eight identities of symmetry in three variables related to generalized twisted Bernoulli polynomials and generalized twisted power sums, both of which are twisted by ramified roots…

Some identities on modified degenerate q-Bernoulli polynomials and numbers

- Mathematics
- 2017

Kim introduced some identities on degenerate q-Bernoulli polynomials, which care defined by the p-adic q-integral on Zp (see [17]). And Kim et al. [10] gave symmetric identities for such polynomials…

Some symmetric identities on higher order q-Euler polynomials and multivariate fermionic p-adic q-integral on Zp

- MathematicsAppl. Math. Comput.
- 2013

Some identities of degenerate q-Euler polynomials under the symmetry group of degree n

- Mathematics
- 2016

In this paper, we derive some interesting identities of symmetry for the degenerate q-Euler polynomials under the symmetry group of degree n arising from the fermionic p-adic q-integral on Zp. c…

## References

SHOWING 1-8 OF 8 REFERENCES

Symmetry p-adic invariant integral on ℤ p for Bernoulli and Euler polynomials

- Mathematics
- 2007

The main purpose of this paper is to investigate several further interesting properties of symmetry for the p-adic invariant integrals on ℤ p . From these symmetry, we can derive many interesting…

On the Symmetries of the -Bernoulli Polynomials

- Mathematics
- 2008

Kupershmidt and Tuenter have introduced reflection symmetries
for the 𝑞-Bernoulli numbers and the Bernoulli polynomials in (2005), (2001),
respectively. However, they have not dealt with…

A Symmetry of Power Sum Polynomials and Bernoulli Numbers

- MathematicsAm. Math. Mon.
- 2001

If one solves the system of linear equations (4) for a, b, and c, the representation given in the theorem follows, and one sees at once that every number triple a,b, c is a Pythagorean triple of n-polygonal numbers.

Applications of a Recurrence for the Bernoulli Numbers

- Mathematics
- 1995

Abstract We give an easy proof of a recently published recurrence for the Bernoulli numbers and we present some applications of the recurrence. One of the applications is a simple proof of the…

Twisted (h,q)-Bernoulli numbers and polynomials related to twisted (h,q)-zeta function and L-function☆

- Mathematics
- 2006

Ultrametric Calculus: An Introduction to p-Adic Analysis

- Mathematics
- 1984

Frontispiece Preface Part I. Valuations: 1. Valuations 2. Ultrametrics Part II. Calculus: 3. Elementary calculus 4. Interpolation 5. Analytic functions Part III. Functions on Zp: 6. Mahler's base and…