Wednesday, 20 April 2011

zeta(1)

The Riemann zeta function is defined by the infinite series


where s is a complex variable with Re(s) > 1.  But if evaluated at 1, it becomes the harmonic series


Despite its divergence, Euler approved the significance of the identity.  The fact that it is connected to all prime numbers* is fascinating.

*It is a well known fact that there are infinitely many primes.

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