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Transformations of Gauss hypergeometric functions

Transformations of Gauss hypergeometric functions
The paper classifies algebraic transformations of Gauss hypergeometric functions and pull-back transformations between hypergeometric differential equations. This classification recovers the classical transformations of degree 2, 3, 4, 6, and finds other transformations of some special classes of the Gauss hypergeometric function.
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Convexity properties related to Gauss hypergeometric function

We investigate the convexity property on $(0,1)$ of the functions $φ_{a,b,c}$ and $1/φ_{a,b,c}$, where $$φ_{a,b,c}(x)= \frac{c-\log(1-x)}{\,_2F_1(a,b,a+b,x)},$$ whenever $a,b\geq 0$ and $a+b\leq 1$. We Show that $φ_{a,b,c}$ (respectively $1/φ_{a,b,c}$) is strictly convex on $(0,1)$ if and only if $c\leq -2γ-ψ(a)-ψ(b),$ (respectively $c\geqα_0$) and $φ_{
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Performance analysis over q-Weibull fading channels for symbol error probability evaluation using a tighter Gaussian Q approximation. [PDF]