Math
Injectivity of $f(x)=\frac{1}{\Gamma(x)\,\eta(x)}\int_{0}^{\infty}\frac{2(\cos(k\ln t))^{2}\,t^{x-1}}{e^{t}+1}\,dt$ on $(0,1)$
Step-by-step mathematics solution: Injectivity of $f(x)=\frac{1}{\Gamma(x)\,\eta(x)}\int_{0}^{\infty}\frac{2(\cos(k\ln t))^{2}\,t^{x-1}}{e^{t}+1}\,dt$ on $
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1. What the problem asks, in plain language
We are given
[ f(x)=\frac{J(x)}{G(x)},\qquad G(x)=\Gamma (x)\,\eta (x),\qquad J(x)=\int_{0}^{\infty}\frac{2\bigl
Original question: Injectivity of $f(x)=\frac{1}{\Gamma(x)\,\eta(x)}\int_{0}^{\infty}\frac{2(\cos(k\ln t))^{2}\,t^{x-1}}{e^{t}+1}\,dt$ on $(0,1)$ on Mathematics Stack Exchange, licensed CC BY-SA.