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Symmetry identities for generalized twisted Euler polynomials twisted by unramified roots of unity. (English) Zbl 1346.11022

Summary: We derive eight identities of symmetry in three variables related to generalized twisted Euler polynomials and alternating generalized twisted power sums, both of which are twisted by ramified roots of unity. 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 integral expression of the generating function for the generalized twisted Euler polynomials and the quotient of \(p\)-adic integrals that can be expressed as the exponential generating function for the alternating generalized twisted power sums.

MSC:

11B68 Bernoulli and Euler numbers and polynomials
11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
05A19 Combinatorial identities, bijective combinatorics
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