Integral using the Hyperbolic Sine Click on the image for a detailed proof \zeta(s)=\frac{2^{s-1}}{\Gamma(s+1)}\int_{0}^{\infty}\frac{x^s}{\sinh(x)^2}dx Copy to Clipboard \zeta(s)=\frac{2^{s-1}}{\Gamma(s+1)}\int_{0}^{\infty}\frac{x^s}{\sinh(x)^2}dx This is one of the first discovered Formulas linking the Riemann Zeta and the Hyperbolic sine.The demonstration we explain is based on the Relation to the Gamma Function 1. Any questions? Feel free to contact our authors at: [email protected], you will be put directly in touch with the person who wrote the text. Didn’t find what you were looking for? Keep looking through all our formulas regarding the Riemann Zeta Function! First Functional EquationLaurent ExpansionEuler's Product Formula First DerivativeAnalytic continuation for 0<Re s<1Relation to the Gamma Function 1 See all Formulas for the Riemann Zeta… X-twitter Pinterest