ANALYTICAL EXPRESSIONS FOR THE EXACT CURVED SURFACE AREA AND VOLUME OF AN ELLIPTIC PARABOLOID VIA MELLIN-BARNES TYPE CONTOUR INTEGRATION

Résumé

In this article, we aim at obtaining the analytical expressions (not previously
found and not recorded in the literature) for the exact curved surface
area of an elliptic paraboloid in terms of Appell’s double hypergeometric function
of second kind. The derivation is based on Mellin-Barnes type contour integral representations
of generalized hypergeometric function pFq(z), Meijer’s G-function and
analytic continuation formula for Gauss function. Moreover, we also obtain the closed
expression for the volume of an elliptic paraboloid. Some special cases related to right
circular paraboloid are also discussed. The closed forms for the exact curved surface
area and volume of an elliptic paraboloid are also verified numerically by using Mathematica
Program.