Abstract
In this paper, we introduce a new family of functions, which is called the Changhee-Genocchi polynomials. We study some explicit identities on these polynomials, which are related to Genocchi polynomials and Changhee polynomials. Also, we represent Changhee-Genocchi polynomials by gamma and beta functions. We also study some properties of higher-order Changhee-Genocchi polynomials related to Changhee polynomials and Daehee polynomials.
Highlights
The Genocchi polynomials are defined by the generating function t et + ext = ∞ tn Gn(x) n! . ( ) nWhen x =, Gn = Gn( ) are called the Genocchi numbers
1 Introduction The Genocchi polynomials are defined by the generating function
We introduce a new family of functions, which is called the ChangheeGenocchi polynomials
Summary
1 Introduction The Genocchi polynomials are defined by the generating function (see [ , ]) We consider Changhee-Genocchi polynomials defined by the generating function log( + t) ( + t)x = +t tn CGn(x) n! When x = , CGn = CGn( ) are called the Changhee-Genocchi numbers. We represent Changhee-Genocchi polynomials by gamma and beta functions.
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