Hurwitz zeta function
evaluates the Hurwitz zeta
function for the numeric or symbolic inputs Z
= hurwitzZeta(s
,a
)s
and
a
. The Hurwitz zeta function is defined only if s
is
not 1 and a
is neither 0 nor a negative integer.
Floating-point evaluation of the Hurwitz zeta function can be slow for complex
arguments or high-precision numbers. To increase the computational speed, you can reduce
the floating-point precision by using the vpa
and digits
functions. For more information, see
Increase Speed by Reducing Precision.
The Hurwitz zeta function is related to other special functions. For example, it can be expressed in terms of the polylogarithm Lis(z) and the gamma function Γ(z):
Here, Re(s) > 0 and Im(a) > 0, or Re(s) > 1 and Im(a) = 0.
[1] Olver, F. W. J., A. B. Olde Daalhuis, D. W. Lozier, B. I. Schneider, R. F. Boisvert, C. W. Clark, B. R. Miller, and B. V. Saunders, eds., Chapter 25. Zeta and Related Functions, NIST Digital Library of Mathematical Functions, Release 1.0.20, Sept. 15, 2018.