Asian Research Journal of Mathematics 13(4): 1-11, 2019; Article no.ARJOM.49152 ISSN: 2456-477X _____________________________________ *Corresponding author: E-mail: pooja.singh@msit.in; Hypergeometric Functions on Cumulative Distribution Function Pooja Singh 1* 1 Maharaja Surajmal Institute of Technology, Guru Gobind Singh Indraprastha University (GGSIPU), Delhi, India. Author’s contribution The sole author designed, analysed, interpreted and prepared the manuscript. Article Information DOI: 10.9734/ARJOM/2019/v13i430114 Editor(s): (1) Dr. Danilo Costarelli, Department of Mathematics and Computer Science, University of Perugia, Italy. Reviewers: (1) Leonardo Simal Moreira, UniFoa – Centro Universitário de Volta Redonda, Brazil. (2) Abdullah Sonmezoglu, Yozgat Bozok University,Turkey. (3) Dr. Khong Wei Leong, Universiti Malaysia Sabah, Malaysia. Complete Peer review History: http://www.sdiarticle3.com/review-history/49152 Received: 09 March 2019 Accepted: 15 May 2019 Published: 23 May 2019 _______________________________________________________________________________ Abstract Exponential functions have been extended to Hypergeometric functions. There are many functions which can be expressed in hypergeometric function by using its analytic properties. In this paper, we will apply a unified approach to the probability density function and corresponding cumulative distribution function of the noncentral chi square variate to extract and derive hypergeometric functions. Keywords: Generalized hypergeometric functions; cumulative distribution theory; chi-square distribution on non-centrality parameter. 1 Introduction Higher-order transcendental functions are generalized from hypergeometric functions. Hypergeometric functions are special function which represents a series whose coefficients satisfy many recursion properties. These functions are applied in different subjects and ubiquitous in mathematical physics and also in computers as Maple and Mathematica. They can also give explicit solutions to problems in economics having dynamic aspects. Original Research Article