Kim, Dae San; Lee, Nari; Na, Jiyoung; Park, Kyoung Ho Identities of symmetry for higher-order Euler polynomials in three variables. I. (English) Zbl 1318.11035 Adv. Stud. Contemp. Math., Kyungshang 22, No. 1, 51-74 (2012). 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). Cited in 1 ReviewCited in 14 Documents 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.) Keywords:higher-order Euler polynomials in three variables; alternating power sums; fermionic integral; identities of symmetry Citations:Zbl 1213.11047 PDFBibTeX XMLCite \textit{D. S. Kim} et al., Adv. Stud. Contemp. Math., Kyungshang 22, No. 1, 51--74 (2012; Zbl 1318.11035)