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I'm new in using bootstrapping, but the relationship used to recover the discount function $v(t,t_m)$ from the price of the bond $P(t,T:c)$ and the coupon $c$ is $v(t,t_m)=\frac{P(t,T:c)-c\sum_{i=1}^{m-1}v(t,t_i)}{1+c}$