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Identities of symmetry for generalized Euler polynomials. (English) Zbl 1262.11022

Summary: We derive eight basic identities of symmetry in three variables related to generalized Euler polynomials and alternating generalized power sums. All of these are new, since there have been results only about identities of symmetry in two variables. The derivations of identities are based on the \(p\)-adic fermionic integral expression of the generating function for the generalized Euler polynomials and the quotient of integrals that can be expressed as the exponential generating function for the alternating generalized power sums.

MSC:

11B68 Bernoulli and Euler numbers and polynomials
11B65 Binomial coefficients; factorials; \(q\)-identities
11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
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