Third and higher order convolution identities for Cauchy numbers

Author:

Komatsu Takao1,Simsek Yilmaz2

Affiliation:

1. Wuhan University, School of Mathematics and Statistics, Wuhan, China

2. University of Akdeniz Faculty of Science, Department of Mathematics, Antalya, Turkey

Abstract

The n-th Cauchy number cn (n ? 0) are defined by the generating function x/ln(1+x)=??,n=0 cnxn=n!. In this paper, we deal with formulae of the type ?l1+...+lm=? l1,...,lm?0 ?!/l1!...lm! (cl1 +...+ clm )n = a0cn+? + ...+ am-1cn+?-m+1, where the ai are suitable rational numbers, the ci are Cauchy numbers and (cl1+...+clm )n := ?k1+...+km=n k1,...,km?0 n!/k1!...km! ck1+l1...ckm+lm. In particular, we give explicit formulae for m = 3 and m = 4.

Publisher

National Library of Serbia

Subject

General Mathematics

Cited by 6 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

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