A new combinatorial identity for Bernoulli numbers and its application in Ramanujan's expansion of harmonic numbers

Abstract

We establish a new combinatorial identity related to the well-known Bernoulli
numbers, which generalizes the result due to Feng and Wang. By means of the
identity, we nd a recursive formula for successively determining the coecients of
Ramanujan's asymptotic expansion for the generalized harmonic numbers.