Finding Zeta(2) with Residues
We give another example of evaluating an infinite series by using residues. We find the exact value of the Riemann Zeta Function at the point two by integrating the complex valued function z^{-2} \pi \cot(\pi z) around a square contour that tends to infinity. We give yet another proof of the exact value of the sum of the reciprocals of squares! The other proofs can be found here:
https://youtu.be/lLOajUF3EVs
#mikethemathematician, #mikedabkowski, #profdabkowski, #complexanalysis, #Riemannzeta
Видео Finding Zeta(2) with Residues канала Mike, the Mathematician
https://youtu.be/lLOajUF3EVs
#mikethemathematician, #mikedabkowski, #profdabkowski, #complexanalysis, #Riemannzeta
Видео Finding Zeta(2) with Residues канала Mike, the Mathematician
mike the mathematician mike dabkowski math complex analysis complex analysis course complex analysis solutions holomorphic function Stein Shakarchi proofs Stein Shakarchi solutions applications of the residue theorem evaluating infinite series infinite series exact value of an infinite series series with residues find the sum of the series hyperbolic cotangent Riemann Zeta Function Riemann Hypothesis Riemann Zeta at 2 sum of reciprocals of squares zeta(2)
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15 мая 2025 г. 9:01:05
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