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Many special functions appear as solutions of differential equations or integrals of elementary functions. Most special functions have relationships with representation theory of Lie groups.

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The existence of an interval $I\subset (0.8856,+\infty)$ such that the derivative $(\Gamma^{... [closed]

The principal inverse function of the gamma function is denoted by $\Gamma^{-1}$. See the paper: Uchiyama - The principal inverse of the gamma function. $\Gamma^{-1}$ is an increasing and concave fun …
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