Jñānābha, Vol. 50 (2) (2020), (132-138)
HYPERGEOMETRIC FORMS OF CERTAIN COMPOSITE FUNCTIONS INVOLVING ARCSINE(x) USING MACLAURIN SERIES AND THEIR APPLICATIONS
By
Aarif Hussain Bhat⋆, M. I. Qureshi and Javid Majid
Department of Applied Sciences and Humanities
Faculty of Engineering and Technology
Jamia Millia Islamia (A Central University), New Delhi -110025, India
Email: miqureshi_delhi@yahoo.co.in
⋆Corresponding author: Email: aarifsaleem19@gmail.com
(Received : July 02, 2019 ; Revised: August 18, 2020)
DOI: https://doi.org/10.58250/jnanabha.2020.50217
In this article, we obtain hypergeometric forms of some composite functions containing arcsine (x) like:
by using Leibniz theorem for successive differentiation, Maclaurin’s series expansion and Taylor’s series expansion, as the proof of the hypergeometric forms of the above functions is not available in the literature.
2010 Mathematics Subject Classifications: 33C05, 34A35, 41A58, 33B10.
Keywords and phrases: Hypergeometric function; Maclaurin’s series; Taylor’s series; Leibniz theorem.