The Riemann Zeta function:

Zeta is defined for all values of x except x = 1 where it is infinite.

For example, Zeta(2) = 1 + 1/4 + 1/9 + 1/16 + ... = Pi^2/6 = 1.64493,40668,48226,43647... .

Here are some notes from my program XPCalc - Extra Precision Floating-Point Calculator http://www.oocities.org/hjsmithh/download.html#XPCalc :

Zeta(x) = Riemann Zeta function:

The Riemann Zeta function of x > 1 is defined by the infinite series 1 + 1/2^x + 1/3^x + 1/4^x + ... .

It is evaluated by first computing the eta function and then using the identity:

which is good for all x except x = 1 where Zeta(x) is infinite. Zeta(0) = −1/2. Zeta(2) = Pi^2/6. Zeta(3) = Z = 1.202056903159594285399738161511449990765... . Zeta(x) = 0 for all negative even integers.

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Changes last made on Monday, 06-Aug-07 20:47:35 PDT