Generalized hypergeometric functions at unit argument

Abstract

The analytic continuation near z = 1 z = 1 of the hypergeometric function p + 1 F p ( z ) _{p + 1}{F_p}\left ( z \right ) is obtained for arbitrary p = 2 , 3 , … , p = 2,3, \ldots , , including the exceptional cases when the sum of the denominator parameters minus the sum of the numerator parameters is equal to an integer.