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(2) The log-behavior of the functions $\\theta(x)=\\sqrt[x]{2 \\zeta(x)\\Gamma(x+1)}$ and $F(x)=\\sqrt[x]{\\frac{\\Gamma(ax+b+1)}{\\Gamma(c x+d+1)\\Gamma(e x+f+1)}}$ is considered, where $\\zeta(x)$ and $\\Gamma(x)$ are the Riemann zeta function and the Euler Gamma function, respectively. 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