zeta¶
Purpose¶
Computes the Riemann Zeta function.
Format¶
-
f =
zeta
(z)¶ - Parameters:
z (NxK matrix) – data. z may be complex
- Returns:
f (NxK matrix) –
Example¶
f = zeta(2);
After the above code, f will equal:
1.6449341
which is equivalent to \(\frac{\pi^2}{6}\).
Remarks¶
The Riemann zeta function is represented by the equation:
\[\zeta(s) = \frac{1}{\Gamma(s)} \int_0^\infty \frac{x^{s-1}}{e^x-1} dx\]
Euler MacLaurin series.
References¶
Jon Breslaw, 2009