Abstract
In this paper, we discuss the properties of a class of Genocchi numbers by generating functions and Riordan arrays, we establish some identities involving Genocchi numbers, the Stirling numbers, the generalized Stirling numbers, the higher order Bernoulli numbers and Cauchy numbers. Further, we get asymptotic value of some sums relating the Genocchi numbers.
Highlights
Introduction and preliminaries The Genocchi numbersGn are defined by t∞ tn et + = Gn n! . n=The relationship between the Genocchi numbers Gn and the Bernoulli numbers Bn and the Euler polynomials En(x) isGn = – n Bn = nEn– ( ) for n ≥ .They are known as follows [ ]
Genocchi numbers and Genocchi polynomials are prolific in the mathematical literature, and many results on Genocchi numbers and Genocchi polynomials identities may be seen in the papers [ – ]
We will mainly study the products of Genocchi numbers Gn(k) with the following forms: Gn(k) n!
Summary
We will mainly study the products of Genocchi numbers Gn(k) with the following forms: Gn(k) n! Properties of products of Genocchi numbers we obtain some properties for Gn(k) by means of the method of generating functions and the Euler transformation. In the first and the last formulas completes the proof.
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