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Chowla-Selberg Lattice Summation {#A}
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Chowla-Selberg lattice summation formula involves evaluation of Epstein zeta function [@Chowla-Selberg] $$\begin{aligned}
\label{eqn:ap1}
 Z(s)=\Sigma^{'} (am^2+bmn+cn^2)^{-s},\end{aligned}$$ where $s$ is a complex number, and the summation is for all integers $m,n$ (each going from $-\infty$ to $+\infty$), while the prime indicates that $m=n=0$ is excluded from the summation; further $a>0$ and $c>0$, while $b$ is real number and subject to the condition that the ‘determinant’ $\triangle=4ac-b^2>0$. This is called lattice summation because the summation is over the lattice points ($\{m,n\}$) on the two-dimensional $m-n$ plane. The Epstein zeta function $Z(s)$ expressed in terms of the lattice summation over $m$ and $n$ in Eq. , is defined for $\Re[s]>1$, and can be continued analytically over the whole s-plane, and satisfies a functional equation similar to the one satisfied by the Riemann zeta Function [@Chowla-Selberg]. Such an analytic continuation, in the context of Casimir effect on 