Abundant symmetry for higher-order Bernoulli polynomials (II)
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We derive twenty five basic identities of symmetry in three vari-ables related to higher-order Bernoulli polynomials and power sums. Thisdemonstrates that there are abundant identities of symmetry in the threevariable 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 symmetryin two variables. The derivations of identities are based on the p-adic integralexpression of the generating function for the higher-order Bernoulli polyno-mials and the quotient of integrals that can be expressed as the exponentialgenerating function for the power sums.
Abstract
We derive twenty five basic identities of symmetry in three vari-ables related to higher-order Bernoulli polynomials and power sums. Thisdemonstrates that there are abundant identities of symmetry in the threevariable 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 symmetryin two variables. The derivations of identities are based on the p-adic integralexpression of the generating function for the higher-order Bernoulli polyno-mials and the quotient of integrals that can be expressed as the exponentialgenerating function for the power sums.
참고문헌 (9)
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