Integrals of products of Hurwitz zeta functions and the Casimir effect in ${\varphi }^4$ field theories

M. A. Shpot, M. P. Chaudhary, R. B. Paris

We evaluate two integrals over $x\in [0,1]$ involving products of the function ${\zeta }_1(a,x)\equiv \zeta (a,x)-x^{-a}$ for $\Re (a)>1$, where $\zeta (a,x)$ is the Hurwitz zeta function. The eval…