HYPERGEOMETRIC FORM OF (1 + x2)ib/2 exp(b tan-1 x) AND ITS APPLICATIONS
By
M. I. Qureshi, Aarif Hussain Bhat? and Javid Majid
Department of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamia Millia
Islamia (A Central University), New Delhi, India-110025
Email: miqureshi delhi@yahoo.co.in, javidmajid375@gmail.com, *
Corresponding author: Email: aarifsaleem19@gmail.com
(Received: March 05, 2022; Informat: May 10, 2022; Revised: January 30, 2023; Accepted January 31, 2023)
DOI: https://doi.org/10.58250/jnanabha.2023.53110
Abstract
In this article, we obtain hypergeometric forms (not available in the literature) of some composite functions like:
(1-y2)d/2 exp(d tanh-1 y), (1+ x2 )g/2 cos(g tan-1 x), (1+ x2 )g/2 sin(g tan-1 x),
(1+ x2 )ik/2 cosh(k tan-1 x), (1+ x2 )ik/2 sinh(k tan-1 x), (1- y2 )g/2 cosh(g tanh-1 y),
(1- y2 )g/2 sinh(g tanh-1 y), (1- y2 )ik/2 cos(k tanh-1 y), (1- y2 )ik/2 sin(k tanh-1 y),
by using Leibniz theorem for successive differentiation and Maclaurin’s series expansion. Some applications are also discussed.
2020 Mathematical Sciences Classification: 33C05, 34A35, 41A58, 33B10.
Keywords and Phrases: Hypergeometric function; Maclaurin series; Leibniz theorem..