A note on the Virasoro blocks at order 1 / c

We derive an explicit expression for the 1/c con- tribution to the Virasoro blocks in 2D CFT in the limit of large c with fixed values of the operators’ dimensions. We follow the direct approach of orthonormalising, at order 1/c, the space of the Virasoro descendants to obtain the blocks as a series expansion around z = 0. For generic conformal weights this expansion can be summed in terms of hyperge- ometric functions and their first derivatives with respect to one parameter. For integer conformal weights we provide an equivalent expression written in terms of a finite sum of undif- ferentiated hypergeometric functions. These results make the monodromies of the blocks around z = 1 manifest.