A classical result in the theory of elliptical functions states that. The functionK2belongs to an important class of functions called the Schwarzian triangle function, for it maps a curvilinear triangle conformally to the upper half plane. The above identity reveals an interesting relation between a hypergeometric function and a Schwarzian triangle function. The purpose of this paper is to clarify the connection between the hypergeometric functionF((1/2 − (1/2n), (1/2) + (1/2n), 1,zand the associated Schwarzian triangle function. In particular, in Theorem 2, we prove that all the major features of the above classical result remain valid for a class of hypergeometric functions called the Legendre functions.