Identities of symmetry for Bernoulli polynomials and power sums

Abstract

Abstract Identities of symmetry in two variables for Bernoulli polynomials and power sums had been investigated by considering suitable symmetric identities. T. Kim used a completely different tool, namely the p-adic Volkenborn integrals, to find the same identities of symmetry in two variables. Not much later, it was observed that this p-adic approach can be generalized to the case of three variables and shown that it gives some new identities of symmetry even in the case of two variables upon specializing one of the three variables. In this paper, we generalize the results in three variables to those in an arbitrary number of variables in a suitable setting and illustrate our results with some examples.

Keywords

• Bernoulli polynomial
• Power sum
• p-adic Volkenborn integral