Yes, that works for non-integer arguments -- provided that the standard series
for zeta converges there. Elsewhere, analytic continuation (that can be
provided by explicit formulas) is required.
Look at, the apparently wildly oscillating values:
0.5j1 zeta 1e5
_157.17j234.337
0.5j1 zeta 1e6
885.57j_127.297
0.5j1 zeta 1e7
_2168.58j_1816.38
In actuality, zeta of 0.5j1 should be (to 16 digits):
0.1439364270771891j-0.7220997435316731
On 9 Mar 2014 12:25:42 -0600, Dan Abell <[email protected]> wrote:
> so
>
> zeta =: [:+/(%@^~>:@i.)
>
> then
>
> 2 zeta 2e5
> 1.64493
> 3 zeta 1e5
> 1.20206
>
> this also works for non-integer arguments:
>
> 3.5 zeta 1e5
> 1.12673
> 3.5j0.5 zeta 1e5
> 1.11256j_0.053509
>
> Cheers,
> -Dan
>
> On 9 Mar 2014, at 11:54, Aai wrote:
>
>> in fact something like:
>>
>> 2 +/@:(%@^~) 1+i.100000
>> 1.64492
——
Murray Eisenberg [email protected]
Mathematics & Statistics Dept.
Lederle Graduate Research Tower phone 240 246-7240 (H)
University of Massachusetts
710 North Pleasant Street
Amherst, MA 01003-9305
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