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

Document Type : Research Paper

Authors

1 Centre for Mathematical and Statistical Sciences (CMSS), Peechi, Thrissur-680653, Kerala, India

2 Department of Mathematics, Aligarh Muslim University, Aligarh-202002, U.P., India

3 Department of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia (A Central University), New Delhi-110025, India.

Abstract

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.

Keywords

References

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History

  • Receive Date: 12 June 2022
  • Revise Date: 25 July 2022
  • Accept Date: 14 August 2022

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