Abundant symmetry for higher-order Bernoulli polynomials (I)
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We derive thirty one basic identities of symmetry in three variables related to higher-order Bernoulli polynomials and power sums. This demonstrates that there are abundant identities of symmetry in the three variable case, in contrast to the two variable case, where there are only a few. 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 higher-order Bernoulli polynomials and the quotient of integrals that can be expressed as the exponential generating function for the power sums.
Abstract
We derive thirty one basic identities of symmetry in three variables related to higher-order Bernoulli polynomials and power sums. This demonstrates that there are abundant identities of symmetry in the three variable case, in contrast to the two variable case, where there are only a few. 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 higher-order Bernoulli polynomials and the quotient of integrals that can be expressed as the exponential generating function for the power sums.
참고문헌 (9)
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