  Sums of positive integer powers have captivated the attention of
mathematicians since ancient times. Over the centuries, mathematicians from
diverse backgrounds have provided expressions for the sum of positive integer
powers of the first $n$ positive integers. In this paper, we contribute to this
endeavour by deriving Bernoulli's formula for $\sum_{k=1}^n k^p,$ for all
positive integers $n$ and nonegative integers $p$, through the utilization of
the Hermite integral representation of the Hurwitz zeta function.

General Mathematics