Formula using the Polygamma Function
Click on the image for a detailed proof
\zeta(m+s)=(-1)^{m-1}\frac{\sin(\pi s)}{\pi} \frac{\Gamma(s)}{\Gamma(s+m)}\int_{0}^{\infty}\psi^{(m)}(1+x)\frac{dx}{x^s}
In his 1937 Article “Integralen voor de zeta-functie van Riemann, ” N.G. de Bruijn obtained a series of formulas connecting the Riemann Zeta to the Digamma and Polygamma functions.
The findings demonstrated a deeper connection between the Zeta function and the Gamma function. The other formulas from the article are the Formulas using the Digamma Function.
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!
