zeta

zeta (a, b [, terms])

The zeta function returns the Hurwitz Zeta function for real or complex arguments a and b

$$\begin{array}{l} \zeta(a, b)=\displaystyle \sum_{k=0}^{\infty} \frac{1}{(k+b)^{a}}, \\ \\ \Re(a)>1, \\ \\ b \neq 0,-1,-2, \ldots \end{array}$$

The Riemann zeta function is the special case:

$$\displaystyle \zeta(a)=\zeta(a, 1) .$$

The zeta function was added in Igor Pro 7.00.

Parameters

The terms parameter defaults to 40. In practice evaluation may terminate before the specified number of terms when convergence is achieved.

References

Olver, Frank W. J.; Lozier, Daniel W.; Boisvert, Ronald F.; Clark, Charles W., eds., "NIST Handbook of Mathematical Functions", 607 pp., Cambridge University Press, 2010.

See Also

Dilogarithm