The Complex Extension of the Riemann Zeta Function

We consider a p-series. We then extend the p-series to the portion of the complex plane where the real part of the complex number is greater than one. This function is the Riemann Zeta Function! We prove that it is related to the Gamma function. We use this connection to prove that the Riemann Zeta function can be extended to a meromorphic function on the complex plane with poles at z=0 and z=1. We discuss the critical strip and the Riemann Hypothesis.

#mikethemathematician, #mikedabkowski, #profdabkowski, #complexanalysis, #riemannzeta

Видео The Complex Extension of the Riemann Zeta Function канала Mike, the Mathematician