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Identities of symmetry for higher-order Euler polynomials in three variables. I. (English) Zbl 1318.11035

Summary: We derive thirty-one basic identities of symmetry in three variables related to higher-order Euler polynomials and alternating power sums. This demonstrates that there are abundant identities of symmetry in three-variable case, in contrast to two-variable case, where there are only a few. These are all 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 higher-order Euler polynomials and the quotient of integrals that can be expressed as the exponential generating function for the alternating power sums.
For Part II, see J. Math. Anal. Appl. 379, No. 1, 388–400 (2011; Zbl 1213.11047).

MSC:

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

Citations:

Zbl 1213.11047
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