Identities of Symmetry for q-Euler Polynomials

Dae San Kim

doi:10.4236/ojdm.2011.11003

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Open Journal of Discrete Mathematics > Vol.1 No.1, April 2011

Identities of Symmetry for q-Euler Polynomials ()

Dae San Kim

DOI: 10.4236/ojdm.2011.11003 PDF HTML 7,716 Downloads 14,531 Views Citations

Abstract

In this paper, we derive eight basic identities of symmetry in three variables related to q-Euler polynomials and the q -analogue of alternating power sums. These and most of their corollaries are new, since there have been results only about identities of symmetry in two variables. These abundance of symmetries shed new light even on the existing identities so as to yield some further interesting ones. The derivations of identities are based on the p-adic integral expression of the generating function for the q -Euler polynomials and the quotient of integrals that can be expressed as the exponential generating function for the q -analogue of alternating power sums.

Keywords

q -Euler Polynomial, q -Analogue of Alternating Power sum, Fermionic Integral, Identities of Symmetry

Share and Cite:

D. Kim, "Identities of Symmetry for q-Euler Polynomials," Open Journal of Discrete Mathematics, Vol. 1 No. 1, 2011, pp. 22-31. doi: 10.4236/ojdm.2011.11003.

Conflicts of Interest

The authors declare no conflicts of interest.

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