Identities of symmetry for higher-order Euler polynomials in three variables (I)
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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 alter-nating power sums.
Abstract
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 alter-nating power sums.
참고문헌 (11)
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