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eng=The Catalan constant, G=Σ^∞_<n=1>[(−1)^k/(2n−1)^2], has attracted much attention and has appeared in various contexts. It is the special value at s=2 of the Dirichlet L-function associated with th...e Gaussian field with its character odd. In this paper, we appeal to the Barnes G-function and a form of the functional equation for the Riemann zeta-function, to deduce an expression for the integral in t/sin t and one for G. These give rise to a corollary which reveals the intrinsicity of the Catalan constant G to the Barnes G-function. We also use one of Ramanujan’s formulas to derive a theorem.続きを見る
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