The Riemann zeta function and tuning/Vector's derivation: Difference between revisions
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i is the imaginary unit, which is on a line perpendicular to the real number line. A complex (two-dimensional) number may be written as a+bi. | i is the imaginary unit, which is on a line perpendicular to the real number line. A complex (two-dimensional) number may be written as a+bi. | ||
With this knowledge, cos(x) can be rewritten as Re(e<sup>ix</sup>) - but since | With this knowledge, cos(x) can be rewritten as Re(e<sup>ix</sup>) - but since we're only doing multiplication and addition and this is the only place complex numbers appear, we can just ignore the Re() and add it back later. | ||
[https://www.desmos.com/calculator/e7wn17tzjf <nowiki>$$ \mu_{c}\left(\sigma, x\right)=\sum_{k=1}^{\infty}\frac{e^{i\left(\ln\left(k\right)x\right)}}{k^{\sigma}} $$</nowiki>] | [https://www.desmos.com/calculator/e7wn17tzjf <nowiki>$$ \mu_{c}\left(\sigma, x\right)=\sum_{k=1}^{\infty}\frac{e^{i\left(\ln\left(k\right)x\right)}}{k^{\sigma}} $$</nowiki>] | ||