Closed form expressions for curved surface area of revolution of hyperbolas: A hypergeometric function approach

Abstract

In this paper, we provide the exact expressions (not found in the liter- ature) for the curved surface area of revolution (about the x-axis and y-axis) of horizontal and oblique hyperbolas. Closed-form expressions for the curved surface area are obtained in terms of Gauss function, Clausen function, and Appell’s hy- pergeometric function of the first kind.