Jñānābha‎, Vol. 50 (2) (2020), (139-145)

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)

 

 

 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.