Recursive structure of the Gauss{} hypergeometric function and boundary/crosscap conformal block

The Gauss{} hypergeometric function shows a recursive structure which resembles those found in conformal blocks. We compare it with the recursive structure of the conformal block in boundary/crosscap conformal field theories that is obtained from the representation theory. We find that the pole structure perfectly agrees but the recursive structure in the Gauss{} hypergeometric function is slightly ``off-shell.