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Abstract and Applied Analysis
Volume 2014, Article ID 289187, 6 pages
http://dx.doi.org/10.1155/2014/289187
Research Article

Euler Polynomials and Combinatoric Convolution Sums of Divisor Functions with Even Indices

1National Institute for Mathematical Sciences, Daejeon 305-811, Republic of Korea
2Département de Mathématiques, Université d'Evry Val d'Essonne, France
3Woosuk University, Samlae, Wanju, Jeonbuk 565-701, Republic of Korea

Received 30 May 2014; Accepted 29 July 2014; Published 27 August 2014

Academic Editor: Elena Litsyn

Copyright © 2014 Daeyeoul Kim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study combinatoric convolution sums of certain divisor functions involving even indices. We express them as a linear combination of divisor functions and Euler polynomials and obtain identities , , and . As applications of these identities, we give several concrete interpretations in terms of the procedural modelling method.