Hurwitz Zeta Function

The Hurwitz Zeta function:

where any term with a + k = 0 is excluded and s > 1.

The ZetaH function is defined for all values of s except s = 1 where it is infinite.

For example, ZetaH(2, 1) = 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 :

ZetaH(s, a) = Hurwitz Zeta function:

The Hurwitz Zeta function of s > 1 is defined by the infinite series 1/a^s + 1/(a+1)^s + 1/(a+2)^s + 1/(a+3)^s + ... .

It is evaluated by ZetaH(s, a) = Lerch(1, s, a).

ZetaH(s, 1) = Zeta(s), the Riemann Zeta function.

And: Wolfram Function Evaluation -- Zeta (2-arg)

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This page accessed times since April 25, 2005.
Page created by: hjsmithh@sbcglobal.net
Changes last made on Monday, 06-Aug-07 20:47:36 PDT

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