Newton series conjecture for the principal inverse gamma function
Let Γ~(x)\tilde{\Gamma}(x)Γ~(x) denote the principal branch of the inverse of the gamma function, so that Γ~(x)=y\tilde{\Gamma}(x)=yΓ~(x)=y when Γ(y)=x \Gamma(y)=xΓ(y)=x. Let α=1.4616… \alpha=1.4616\ldotsα=1.4616… be the unique p…