Further Results on a Function Relevant for Conformal Blocks

We present further mathematical results on a function appearing in the conformal blocks of four-point correlation functions with arbitrary primary operators. The $H$-function was introduced in a previous article and it has several interesting properties. We prove explicitly the recurrence relation as well as the $D_6$-invariance presented previously. We also demonstrate the proper action of the differential operator used to construct the $H$-function.