scholarly journals Univalence and Convexity Properties for Gaussian Hypergeometric Functions

2001 ◽  
Vol 31 (1) ◽  
pp. 327-353 ◽  
Author(s):  
S. Ponnusamy ◽  
M. Vuorinen
Keyword(s):  
Hypergeometric Functions ◽  
Gaussian Hypergeometric Functions ◽  
Convexity Properties

scholarly journals Monotonicity, convexity properties and inequalities involving Gaussian hypergeometric functions with applications

2021 ◽  
Vol 7 (4) ◽  
pp. 4974-4991
Author(s):  
Ye-Cong Han ◽  
◽  
Chuan-Yu Cai ◽  
Ti-Ren Huang ◽  
Keyword(s):  
Hypergeometric Function ◽  
Hypergeometric Functions ◽  
Elliptic Integral ◽  
Gaussian Hypergeometric Function ◽  
Gaussian Hypergeometric Functions ◽  
Convexity Properties

<abstract><p>In this paper, we mainly prove monotonicity and convexity properties of certain functions involving zero-balanced Gaussian hypergeometric function $ F(a, b; a+b; x) $. We generalize conclusions of elliptic integral to Gaussian hypergeometric function, and get some accurate inequalities about Gaussian hypergeometric function.</p></abstract>

scholarly journals Polynomial series expansions for confluent and Gaussian hypergeometric functions

2005 ◽  
Vol 74 (252) ◽  
pp. 1937-1953 ◽  
Author(s):  
W. Luh ◽  
J. Müller ◽  
S. Ponnusamy ◽  
P. Vasundhra
Keyword(s):  
Hypergeometric Functions ◽  
Series Expansions ◽  
Gaussian Hypergeometric Functions ◽  
Polynomial Series

scholarly journals Landen Inequalities for Zero-Balanced Hypergeometric Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Slavko Simić ◽  
Matti Vuorinen
Keyword(s):  
Open Problem ◽  
Hypergeometric Functions ◽  
Elliptic Integral ◽  
Complete Elliptic Integral ◽  
Turn On ◽  
Gaussian Hypergeometric Functions

For zero-balanced Gaussian hypergeometric functionsF(a,b;a+b;x),a,b>0, we determine maximal regions ofabplane where well-known Landen identities for the complete elliptic integral of the first kind turn on respective inequalities valid for eachx∈(0,1). Thereby an exhausting answer is given to the open problem from the work by Anderson et al., 1990.

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