A Note on the Hypergeometric Mean Value
Item
- Title
- Description
- Creator
- Date
- Date Available
- Date Issued
- Identifier
- uri
- Abstract
- Language
- Publisher
- Subject
- Type
-
A Note on the Hypergeometric Mean Value
-
DOI: 10.1007/BF03320978
-
Richards, Kendall C.
-
2018-02-27
-
2018-02-27
-
2001
-
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.
-
https://collections.southwestern.edu/s/suscholar/item/262
-
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.
-
English
-
Computational Methods and Function Theory
-
Hypergeometric function
-
Generalized hypergeometric function
-
Means of order t
-
Article
- Item sets