Analytical expression for the exact curved surface area and volume of a hyperboloid of one sheet via Mellin-Barnes type contour integration

Abstract

In this article, we aim at obtaining the analytical expression ({\bf not previously found and recorded in the literature}) for the exact curved surface area of a hyperboloid of one sheet in terms of Srivastava-Daoust triple hypergeometric function. The derivation is based on Mellin-Barnes type contour integral representations of generalized hypergeometric function${}_p{F}_q(z)$, Meijer's $G$-function, decomposition formula for Meijer's $G$-function and series rearrangement technique. Further, we also obtain the formula for the volume of a hyperboloid of one sheet. The closed forms for the exact curved surface area and volume of the hyperboloid of one sheet are also verified numerically by using {\it Mathematica Program}.

18 pages. arXiv admin note: substantial text overlap with arXiv:2210.02858. text overlap with arXiv:2210.07964