- Hello Don,

> Can someone tell me if the following function is convergent and if so

this sum is convergent, but I can't invent how to calculate it. As for error term, I think, if you take first k terms of the sum instead of infinity, the error will be about 1/log(k).

> what it is convergent to with some degree of precision and an error

> term?

>

> For {n=[1->oo], P=primes[2->oo]} sum{n/Pn^2}

Best wishes,

Andrey

[Non-text portions of this message have been removed] - Can someone tell me if the following function is convergent and if so

what it is convergent to with some degree of precision and an error

term?

For {n=[1->oo], P=primes[2->oo]} sum{n/Pn^2}

It is bascially the Prime zeta P2 but for each next p(rime) the

number on top also increments ie. -

1/2^2 + 2/3^2 + 3/5^2 + 4/7^2 + 5/11^2 + 6/13^2 + 7/17^2 + ...

Also, is this a function already known by some name? Perhaps in

another form - double zeta-P2, second-order zeta-P2, something?

Thanks.