appear in closed forms for circular-cylinder. For more details regarding the Chowla-Selberg lattice summation, see– Appendix-A of Ref. [@Milton2010], and also our Appendix-\[A\]. Another problem with the Chowla-Selberg formula for circular-cylinder is that, it is not even applicable for the McMahon asymptotic forms of $\alpha_{\sigma,n}\rightarrow\pi(\sigma/2+n-1/4)$ and $\beta_{\sigma,n}\rightarrow\pi(\sigma/2+n+1/4)$ [@McMahon] as the ‘determinant’[^1] $\triangle\rightarrow0$. Exact renormalized values of $D^{(2)}$ and $N^{(2)}$ were obtained, within the integral forms of the lattice summations (which do not at all need the values of $\alpha_{\sigma,n}$ and $\beta_{\sigma,n}$) with further subtraction of homogeneous energy eigenvalue $\omega_{\bm k}|_{R\rightarrow\infty}$ from each energy eigenvalue $\omega_{\bm k}$ in Eq. , as [@Milton1999; @Gosdzinsky] $$\begin{aligned}
\label{eqn:13o3}
D^{(2)}=0.000614794033/R^2=0.0019314324176/\pi R^2,\end{aligned}$$ and $$\begin{aligned}
\label{eqn:13o4}
N^{(2)}=-0.01417613719/R^2=-0.0445356485/\pi R^2.\end{aligned}$$ Thus we get the total Casimir (or renormalized vacuum) energy as [@Milton1981; @Gosdzinsky] $$\begin{aligned}
\label{eqn:18}
E_c=L\hbar c[D^{(2)}+N^{(2)}]=-0.013561343{\small{~}}L\hbar c/R^2,\end{aligned}$$ and the Casimir force ($f_R=-\frac{\partial E_c}{\partial R}$) as $$\begin{aligned}
\label{eqn:19a}
f_R=-0.027122686{\small{~}}L\hbar c/R^2.\end{aligned}$$ The Casimir pressure ($p_R=f_R/2\pi RL$) is now given by $p_R\approx-0.0043\frac{\hbar c}{R^4}$, which is reasonably strong as $R$ approaches the atomic dimension. For example, if $R=10~\text{\AA}$, the Casimir pressure is $p_R\approx-1\times10^{8}$ N/m$^2$. Such a strong attractive Casimir pressure can possibly be tested for cylindrical graphene sheet, carbon nano-tube, etc. For a circular waveguide of radius $R=0.1$ mm, on the other 