In the present work we compute explicitly a certain type of hypergeometric functions of matrix variables given as an integral of a Gaussian-type kernel. In the case of one variable, these functions are related to the modified Bessel function of the third kind.

We find a characteristic-free algebraic condition for developability of uniruled varieties. As an application, we study developable varieties over positive characteristic fields. In particular, we generalize classification theorem of one parameter developable ruled varieties to arbitrary characteristic.