Vol. 11, No. 4, 2018

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ISSN: 1944-4184 (e-only)
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Interpolation on Gauss hypergeometric functions with an application

Hina Manoj Arora and Swadesh Kumar Sahoo

Vol. 11 (2018), No. 4, 625–641
Abstract

We use some standard numerical techniques to approximate the hypergeometric function

2F1[a,b;c;x] = 1 + ab c x + a(a + 1)b(b + 1) c(c + 1) x2 2! +

for a range of parameter triples (a,b,c) on the interval 0 < x < 1. Some of the familiar hypergeometric functional identities and asymptotic behavior of the hypergeometric function at x = 1 play crucial roles in deriving the formula for such approximations. We also focus on error analysis of the numerical approximations leading to monotone properties of quotients of gamma functions in parameter triples (a,b,c). Finally, an application to continued fractions of Gauss is discussed followed by concluding remarks consisting of recent works on related problems.

Keywords
interpolation, hypergeometric function, gamma function, error estimate
Mathematical Subject Classification 2010
Primary: 65D05
Secondary: 33B15, 33B20, 33C05, 33F05
Milestones
Received: 21 November 2016
Revised: 7 July 2017
Accepted: 21 July 2017
Published: 15 January 2018

Communicated by Kenneth S. Berenhaut
Authors
Hina Manoj Arora
Discipline of Electrical Engineering
Indian Institute of Technology
Indore
India hina.arora@stonybrook.eduDepartment of Applied Mathematics & Statistics
Stony Brook University
Stony Brook, NY
United States
Swadesh Kumar Sahoo
Discipline of Mathematics
Indian Institute of Technology
Indore
India