Mathematical Physics

   

Is This Euler's Mistake? or is it Just a Misprint Circling?

Authors: Toshiro Takami

Euler's formula is generally expressed as follows. \zeta(1-s)={\frac{2}{(2*pi)^s}\Gamma(s)\cos(\frac{pi*s}{2})\zeta(s))} However, I substitute (-2,-4,-6) in this and do not become zero. There is not it and approaches only for a zero when I surely substitute Non trivial zero point (0.5+14.1347i, 0.5+21.0220i) for this formula. It is either whether the formula of the Euler is wrong whether a misprint is sold as for this.  I am convinced misprints are circulating. I am convinced that it is sold It is make a mistake with cos, and to have printed sin. The one that is right is as follows. \zeta(1-s)={\frac{2}{(2*pi)^s}\Gamma(s)\sin(\frac{pi*s}{2})\zeta(s))}

Comments: 2 Pages.

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Submission history

[v1] 2018-12-02 02:14:47
[v2] 2018-12-04 00:00:37

Unique-IP document downloads: 20 times

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