Functional Equation
The functional equation relates values of the zeta on the left- and right-hand sides of the complex plane. For integers ,
![\zeta \left(1-s,\frac{m}{n} \right) =
\frac{2\Gamma(s)}{ (2\pi n)^s }
\sum_{k=1}^n \left[\cos
\left( \frac {\pi s} {2} -\frac {2\pi k m} {n} \right)\;
\zeta \left( s,\frac {k}{n} \right)\right]](http://upload.wikimedia.org/math/c/7/6/c76111a861d49dae418bc7da47734a6e.png)
holds for all values of s.
Read more about this topic: Hurwitz Zeta Function
Famous quotes containing the words functional and/or equation:
“Well designed, fully functional infant. Provides someone to live for as well as another mouth to feed. Produces cooing, gurgling and other adorable sounds. May cause similar behavior in nearby adults. Cries when hungry, sleepy or just because. Hand Wash with warm water and mild soap, then pat dry with soft cloth and talc. Internal mechanisms are self-cleaning... Two Genders: Male. Female. Five Colors: White. Black. Yellow. Red. Camouflage.”
—Alfred Gingold, U.S. humorist. Items From Our Catalogue, “Baby,” Avon Books (1982)
“A nation fights well in proportion to the amount of men and materials it has. And the other equation is that the individual soldier in that army is a more effective soldier the poorer his standard of living has been in the past.”
—Norman Mailer (b. 1923)