ScalingStacks

Lemma 3.7 . [023A]

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Lemma 3.7.

The function

g(y)=−2F1[12,−1n,n−1n;yn]+p∗w0y,g(y)=-\,_{2}F_{1}[\frac{1}{2},-\frac{1}{n},\frac{n-1}{n};y^{n}]+\frac{p_{*}}{w_{0}}y,

where F12​[a,b,c;z]\,{}_{2}F_{1}[a,b,c;z] is the hypergeometric function (38). In particular,

g⁡(1)=p∗w0−Γ⁡(1−1n)​πΓ⁡(12−1n).g(1)=\frac{p_{*}}{w_{0}}-\frac{\Gamma(1-\frac{1}{n})\sqrt{\pi}}{\Gamma(\frac{1}{2}-\frac{1}{n})}.

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