What would be the asymptotic growth rate of or for the special cases or

I tried using the relation but couldn't get it to work. How many terms would you require to compute and to 20 digits using direct computation??

(Shake)

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- Jan 2nd 2012, 08:22 AMmathematicaphoenixGrowth rate of Prime zeta function
What would be the asymptotic growth rate of or for the special cases or

I tried using the relation but couldn't get it to work. How many terms would you require to compute and to 20 digits using direct computation??

(Shake) - Jan 2nd 2012, 11:13 PMchisigmaRe: Growth rate of Prime zeta function
- Jan 3rd 2012, 05:04 AMmathematicaphoenixRe: Growth rate of Prime zeta function
I got that result. But how would you use (3) to calculate the the number of terms required to get to a given accuracy using direct calculation.

For example, for I have already found that, to get digits of accuracy you would require

terms. I want to do a similar thing with . Can you help?

Thanks

(Hi) - Jan 3rd 2012, 05:37 AMchisigmaRe: Growth rate of Prime zeta function
If You intend to use that formula, then what You can do is to extimate the minimum value of s that gives an error . If You write...

(1)

... then the condition is approximately...

(2)

If You uses two terms of the series writing then You write...

(3)

... and the condition is approximately...

(4)

Now You can proceed increasing the terms till to arrive to the required accuracy...

Kind regards

- Jan 6th 2012, 02:05 AMmathematicaphoenixRe: Growth rate of Prime zeta function
- Jan 6th 2012, 02:33 AMchisigmaRe: Growth rate of Prime zeta function
- Jan 6th 2012, 09:33 PMmathematicaphoenixRe: Growth rate of Prime zeta function