equation, gives rise to the mean-field part of Casimir force. We explicitly compute these two contributions to the Casimir effect.

We begin this article by revisiting the calculation of the Casimir force due to the confinement of electromagnetic field in a hollow conducting circular-cylinder. Bessel functions \[$J_\sigma(\alpha_{\sigma,n}\rho/R)$ and $J_\sigma(\beta_{\sigma,n}\rho/R)$\], Bessel zeros ($\alpha_{\sigma,n};~\sigma=0,\pm1,\pm2,...;~n=1,2,3,...$), and zeros of the first derivatives of the Bessel functions of the first kind ($\beta_{\sigma,n}$) naturally appear in the modes of quantum fluctuations and in the expression of the vacuum energy. To get the Casimir force from the vacuum energy we apply zeta regularization technique prescribed by Gosdzinsky and Romeo [@Gosdzinsky]. Then by applying these techniques, we study the Casimir effect filling the hollow cylinder by an interacting Bose-Einstein condensate for $T \to 0$. For this case, we begin with the calculation of the grand canonical energy of the interacting BEC in terms of its mean-field and quantum fluctuation (discrete Bogoliubov excitation) parts. We explicitly calculate the contribution to the Casimir force arising from the mean-field and quantum fluctuations parts for both the Dirichlet and the Neumann boundary conditions. Thus we study condensate density dependence of the Casimir force. We apply dimensional regularization cum Chowla-Selberg lattice summation technique 