‘We consider two integrals over \(x \in [0,1]\) involving products of the function \(\zeta_{1}(a,x) \equiv \zeta(a,x) − x^{−a}\), where \(\zeta(a,x)\) is the Hurwitz zeta function, given by

\begin{equation}

\int\limits_{0}^{1} \zeta_{1}(a,x) \zeta_{1}(b,x) \mathrm{d}x

\end{equation}

and

\begin{equation}

\int\limits_{0}^{1} \zeta_{1}(a,x) \zeta_{1}(b,1-x) \mathrm{d}x

\end{equation}

when \(\Re (a,b) \gt 1\). These integrals have been investigated recently in [23]; here we provide an alternative derivation by application of Feynman parametrization. We also discuss a moment integral and the evaluation of two doubly infinite sums containing the Riemann zeta function \(\zeta(x)\) and two free parameters a and b. The limiting forms of these sums when \(a+b\) takes on integer values are considered.‘

The paper is available here.