A Note on the Hypergeometric Mean Value

Item

Title
A Note on the Hypergeometric Mean Value
Description
DOI: 10.1007/BF03320978
Creator
Richards, Kendall C.
Date
2018-02-27
Date Available
2018-02-27
Date Issued
2001
Identifier
Barnard, R. W., & Richards, K. C. (September 01, 2001). A Note on the Hypergeometric Mean Value. Computational Methods and Function Theory, 1, 1, 81-88.
uri
https://collections.southwestern.edu/s/suscholar/item/262
Abstract
Recent efforts to obtain bounds for the complete elliptic integral 2 ·2F1−1 2, 1 2 ; 1; r2 in terms of power means and other related means have precipitated the search for similar bounds for the more general 2F1(α, β; γ; r). In an early paper, B. C. Carls considered the approximation of the hypergeometric mean values
( 2F1(−a, b; b + c; r))1/a in terms of means of order t, given by Mt(s, r) :=
{(1 − s) + s(1 − r)t}1/t. In this note, a refinement of one such approximation is established by first proving a general positivity result involving 3F2.
Language
English
Publisher
Computational Methods and Function Theory
Subject
Hypergeometric function
Generalized hypergeometric function
Means of order t
Type
Article