TY - JOUR

T1 - On (h, q)-Daehee numbers and polynomials

AU - Do, Younghae

AU - Lim, Dongkyu

N1 - Publisher Copyright:
© 2015, Do and Lim; licensee Springer.

PY - 2015/12/1

Y1 - 2015/12/1

N2 - 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 the q-analogue of Daehee numbers and polynomials which are called q-Daehee numbers and polynomials. Lim considered the modified q-Daehee numbers and polynomials which are different from the q-Daehee numbers and polynomials of Kim et al. In this paper, we consider (h,q)-Daehee numbers and polynomials and give some interesting identities. In case h = 0, we cover the q-analogue of Daehee numbers and polynomials of Kim et al. In case h = 1, we modify q-Daehee numbers and polynomials. We can find out various (h,q)-related numbers and polynomials which are studied by many authors.

AB - 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 the q-analogue of Daehee numbers and polynomials which are called q-Daehee numbers and polynomials. Lim considered the modified q-Daehee numbers and polynomials which are different from the q-Daehee numbers and polynomials of Kim et al. In this paper, we consider (h,q)-Daehee numbers and polynomials and give some interesting identities. In case h = 0, we cover the q-analogue of Daehee numbers and polynomials of Kim et al. In case h = 1, we modify q-Daehee numbers and polynomials. We can find out various (h,q)-related numbers and polynomials which are studied by many authors.

KW - (h, q)-Bernoulli polynomials

KW - (h, q)-Daehee numbers

KW - (h, q)-Daehee polynomials

KW - p-adic q-integral

UR - http://www.scopus.com/inward/record.url?scp=84926348163&partnerID=8YFLogxK

U2 - 10.1186/s13662-015-0445-3

DO - 10.1186/s13662-015-0445-3

M3 - Article

AN - SCOPUS:84926348163

SN - 1687-1839

VL - 2015

JO - Advances in Difference Equations

JF - Advances in Difference Equations

IS - 1

ER -