Solution
= Solution
Integration by parts, or the identities obtained by splitting $1=t+(1-t)$, gives
$$
B(p,z+1)=\frac z{p+z}B(p,z).
$$
Therefore
$$
\boxed{(p+z)B(p,z+1)=zB(p,z)}.
$$
= Solution
Integration by parts, or the identities obtained by splitting $1=t+(1-t)$, gives
$$
B(p,z+1)=\frac z{p+z}B(p,z).
$$
Therefore
$$
\boxed{(p+z)B(p,z+1)=zB(p,z)}.
$$