2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Slavko Simić ◽  
Matti Vuorinen

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.


2020 ◽  
Vol 14 (1) ◽  
pp. 138-149
Author(s):  
Rakesh Parmar ◽  
Tibor Pogány

The main purpose of this paper is to present closed integral form expressions for the Mathieu-type a-series and for the associated alternating versions whose terms contain a generalized p-extended Gauss' hypergeometric function. Related bounding inequalities for the p-generalized Mathieu-type series are also obtained. Finally, a set of various (known or new) special cases and consequences of the results earned are presented.


2021 ◽  
Vol 7 (4) ◽  
pp. 4974-4991
Author(s):  
Ye-Cong Han ◽  
◽  
Chuan-Yu Cai ◽  
Ti-Ren Huang ◽  

<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>


1999 ◽  
Vol 22 (4) ◽  
pp. 765-773 ◽  
Author(s):  
Yong Chan Kim ◽  
S. Ponnusamy

LetF(a,b;c;z)be the classical hypergeometric function andfbe a normalized analytic functions defined on the unit disk𝒰. Let an operatorIa,b;c(f)be defined by[Ia,b;c(f)](z)=zF(a,b;c;z)*f(z). In this paper the authors identify two subfamilies of analytic functionsℱ1andℱ2and obtain conditions on the parametersa,b,csuch thatf∈ℱ1impliesIa,b;c(f)∈ℱ2.


2009 ◽  
Vol 2009 ◽  
pp. 1-15
Author(s):  
H. Silverman ◽  
Thomas Rosy ◽  
S. Kavitha

The authors define a new subclass of of functions involving complex order in the open unit disk . For this new class, we obtain certain inclusion properties involving the Gaussian hypergeometric functions.


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