Identities of symmetry for q-Euler polynomials

Details Identities of symmetry for q-Euler polynomials Identities of symmetry for q-Euler polynomials

2010-04-09

arxiv.org/abs/1004.1477v1

Mathematics

Number Theory

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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.

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