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Question relating numerical representations, operations and methods, including approximate results instead of exact symbolic results.

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Numerical estimates on a given functional [duplicate]

Consider the following functional : $$ I(x,s) =\int_0^\infty\mathrm dy \frac{F(x + \mathrm iy, s) − F(x −\mathrm iy, s)}{\mathrm e^{2πy}-1}, $$ where $ F(z, s) = \dfrac{\sinh(\sin^2[π\Gamma(z)/(2z)] …
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