On Alzer-Kwong's Identities for Bernoulli polynomials

2020/05/08 by Kim, Min-Soo, Kim, Daeyeoul, So, Ji Suk
#11B68 #11S80 #FOS: Mathematics #H.0 #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2005.03874

Abstract

In this paper, we prove new identities for Bernoulli polynomials that extend Alzer and Kwong's results. The key idea is to use the Volkenborn integral over \mathbb Z_p of the Bernoulli polynomials to establish recurrence relations on the integrands. Also, some known identities are obtained by our approach.

Related

• New results on p-Bernoulli numbers
• Identities of symmetry for higher-order q-Bernoulli polynomials
• Identities of symmetry for Bernoulli polynomials arising from quotients of Volkenborn integrals invariant under S₃
• New identities involving Bernoulli and Euler polynomials
• Identities for the Euler polynomials, p-adic integrals and Witt's formula