Relation to the Gamma Function 5
\zeta(s)=\frac{1}{2}+\frac{1}{s-1}+\frac{1}{\Gamma(s)}\int_{0}^{\infty}\left(\frac{1}{e^x-1}-\frac{1}{x}+\frac{1}{2}\right)\frac{x^{s-1}}{e^x}dx
This Relation connecting the Riemann Zeta and the Gamma Function has the benefit of making explicit the pole of the Zeta Function at s=1.
This demonstration 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!
