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The semileptonic decays $B_c^+\rightarrow P(V) +\ell^++\bar{\nu}_\ell$ and the nonleptonic decays $B_c^+\rightarrow P(V)+L$, where $P(V)$ denotes a pseudoscalar (vector) charmonium or ($\bar{b}s$)-meson, and $L$ denotes a light meson, are studied in the framework of improved instantaneous Bethe-Salpeter (BS) equation and the Mandelstam formula.
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