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How to prove the convergence of the following series involving Gamma function?
Consider the following result（$d$ denotes the dimensions and $0<t<T$）
$$c\left(\sum_{j=0}^\infty\frac{\Gamma^j(1-\kappa)}{\Gamma((j+1)(1-\kappa))}t^{j(1-\kappa)-\kappa}\right)^{\frac{1}{2}}\leq ...
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