Bull. Korean Math. Soc. 2013; 50(4): 1289-1296
Printed July 1, 2013
https://doi.org/10.4134/BKMS.2013.50.4.1289
Copyright © The Korean Mathematical Society.
Hyun-Mee Kim
Kookmin University
Recently, T. Kim has introduced and analysed the $q$-Euler polynomials (see [3, 14, 35, 37]). By the same motivation, we will consider some interesting properties of the $q$-Genocchi polynomials. Further, we give some formulae on the Bernstein and $q$-Genocchi polynomials by using $p$-adic integral on $\mathbb Z_p$. From these relationships, we establish some interesting identities.
Keywords: $q$-Genocchi number, $q$-Genocchi polynomial, Bernstein polynomial, $p$-adic integral
MSC numbers: 11S80, 11B68
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