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Remarks on Sum of Products of https://static-content.springer.com/image/art%3A10.1155%2F2008%2F816129/MediaObjects/13660_2007_Article_1863_IEq1_HTML.gif -Twisted Euler Polynomials and Numbers

Journal of Inequalities and Applications20072008:816129

DOI: 10.1155/2008/816129

Received: 29 March 2007

Accepted: 16 October 2007

Published: 25 November 2007

Abstract

The main purpose of this paper is to construct generating functions of higher-order twisted https://static-content.springer.com/image/art%3A10.1155%2F2008%2F816129/MediaObjects/13660_2007_Article_1863_IEq1_HTML.gif -extension of Euler polynomials and numbers, by using https://static-content.springer.com/image/art%3A10.1155%2F2008%2F816129/MediaObjects/13660_2007_Article_1863_IEq2_HTML.gif -adic, https://static-content.springer.com/image/art%3A10.1155%2F2008%2F816129/MediaObjects/13660_2007_Article_1863_IEq3_HTML.gif -deformed fermionic integral on https://static-content.springer.com/image/art%3A10.1155%2F2008%2F816129/MediaObjects/13660_2007_Article_1863_IEq4_HTML.gif . By applying these generating functions, we prove complete sums of products of the twisted https://static-content.springer.com/image/art%3A10.1155%2F2008%2F816129/MediaObjects/13660_2007_Article_1863_IEq1_HTML.gif -extension of Euler polynomials and numbers. We also define some identities involving twisted https://static-content.springer.com/image/art%3A10.1155%2F2008%2F816129/MediaObjects/13660_2007_Article_1863_IEq1_HTML.gif -extension of Euler polynomials and numbers.

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Authors’ Affiliations

(1)
Department of Mathematics, Faculty of Arts and Science, University of Uludag
(2)
Department of Mathematics, Faculty of Arts and Science, University of Akdeniz

Copyright

© Hacer Ozden et al. 2008

This article is published under license to BioMed Central Ltd. 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.