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We present the semileptonic decay of $B_{c}$ meson in a QCD potential modelwith the coulombic part of the Cornell potential $-\frac{4\alpha_{S}}{3r}+br+c$as perturbation. Computing the slope and curvature of Isgur Wise function inthis approach, we study the pseudoscalar and vector form factors for thetransition of $B_{c}$ meson to its S wave charmonium $c\bar{c}$ states.Numerical estimates of widths for the transitions of $B_{c}\rightarrowJ/\psi(\eta_{c})l\nu_{l}$ are presented. The results are found to be in goodagreement with other theoretical values.

Semileptonic decay of Bc meson into S wave charmonium in a QCD potential model with coulombic part as perturbation