Zeta Function

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Panna Lal Patodia

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Feb 22, 2018, 7:50:54 AM2/22/18
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Though the Zeta function for integer gives accurate result. I got different result for decimal.

For example,
zeta(2.1) = 1.560216533503362015758917170653014234218242329871913719457665460561046377382145741481950840260305962
to 100 decimal places.

However, when I used GP/PARI, I got the following result:

zeta(2.1) = 1.560216533503362083710516769691471924753050995905995862613928931079053836113791436865109088073718989

Both result tallies for 15 decimal place but beyond, the result differs drastically. I don't know which one is correct.

Please check.

Regards,

Panna Lal Patodia

Andrey G. Grozin

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Feb 22, 2018, 8:27:08 AM2/22/18
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On Thu, 22 Feb 2018, Panna Lal Patodia wrote:
> zeta(2.1) = 1.560216533503362015758917170653014234218242329871913719457665460561046377382145741481950840260305962
> to 100 decimal places.
If you literally write zeta(2.1), then python first transforms 2.1 to a
double precision number, which is not exactly equal to 2.1; then it is
transformed by mpmath to a high-precision number which differs from 2.1
after about 15-th decimal place; and then zeta of this number is
calculated. Please write the argument of zeta correctly.

Andrey

Aaron Meurer

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Feb 22, 2018, 3:46:04 PM2/22/18
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It would help to indicate what the correct way is. The correct way is
to specify 2.1 as a string, and wrap it in mpf, like

zeta(mpf('2.1'))

Aaron Meurer

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