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Analytical expression for the exact curved surface area and volume of hyperboloid of two sheets via Mellin-Barnes type contour integration | ||
| Journal of Mahani Mathematical Research | ||
| دوره 12، شماره 2 - شماره پیاپی 25، مرداد 2023، صفحه 77-104 اصل مقاله (1.02 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2022.19659.1275 | ||
| نویسندگان | ||
| M.A. Pathan* 1، 2؛ M. I. Qureshi3؛ Javid Majid3 | ||
| 1Centre for Mathematical and Statistical Sciences (CMSS), Peechi, Thrissur-680653, Kerala, India | ||
| 2Department of Mathematics, Aligarh Muslim University, Aligarh-202002, U.P., India | ||
| 3Department of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia (A Central University), New Delhi-110025, India. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Meijer's $G$-function؛ Mellin-Barnes type contour integrals؛ Hyperboloid of two sheets؛ General triple hypergeometric function of Srivastava؛ Appell's function of second kind؛ Mathematica Program | ||
| مراجع | ||
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