Analytical expression for the exact curved surface area and volume of hyperboloid of two sheets via Mellin-Barnes type contour integration

In this article, we aim at obtaining the analytical expression (not previously found and recorded in the literature) for the exact curved surface area of a hyperboloid of two sheets in terms of Appell's double hypergeometric function of second kind and triple hypergeometric function of Srivasta...

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Bibliographic Details
Published in:Journal of Mahani Mathematical Research Center 2023-05, Vol.12 (2), p.77-104
Main Authors: M.A. Pathan, M. Qureshi, Javid Majid
Format: Article
Language:English
Subjects:
appell's function of second kind
general triple hypergeometric function of srivastava
hyperboloid of two sheets
mathematica program
meijer's $g$-function
mellin-barnes type contour integrals
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Summary:In this article, we aim at obtaining the analytical expression (not previously found and recorded in the literature) for the exact curved surface area of a hyperboloid of two sheets in terms of Appell's double hypergeometric function of second kind and triple hypergeometric function of Srivastava. The derivation is based on Mellin-Barnes type contour integral representations of generalized hypergeometric function$~_pF_q(z)$,  Meijer's $G$-function and series manipulation technique. Further, we also obtain the formula for the volume of hyperboloid of two sheets. The closed forms for the exact curved surface area and volume of the hyperboloid of two sheets are also verified numerically by using  Mathematica Program.
ISSN:2251-7952
2645-4505
DOI:10.22103/jmmr.2022.19659.1275