Open Access
Translator Disclaimer
2018 Interpolation on Gauss hypergeometric functions with an application
Hina Manoj Arora, Swadesh Kumar Sahoo
Involve 11(4): 625-641 (2018). DOI: 10.2140/involve.2018.11.625

Abstract

We use some standard numerical techniques to approximate the hypergeometric function

2 F 1 [ a , b ; c ; x ] = 1 + a b c x + a ( a + 1 ) b ( b + 1 ) c ( c + 1 ) x 2 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.

Citation

Download Citation

Hina Manoj Arora. Swadesh Kumar Sahoo. "Interpolation on Gauss hypergeometric functions with an application." Involve 11 (4) 625 - 641, 2018. https://doi.org/10.2140/involve.2018.11.625

Information

Received: 21 November 2016; Revised: 7 July 2017; Accepted: 21 July 2017; Published: 2018
First available in Project Euclid: 28 March 2018

zbMATH: 06864400
MathSciNet: MR3778916
Digital Object Identifier: 10.2140/involve.2018.11.625

Subjects:
Primary: 65D05
Secondary: 33B15 , 33B20 , 33C05 , 33F05

Keywords: error estimate , Gamma function , hypergeometric function , interpolation

Rights: Copyright © 2018 Mathematical Sciences Publishers

JOURNAL ARTICLE
17 PAGES


SHARE
Vol.11 • No. 4 • 2018
MSP
Back to Top