Trying to calculate the value of pi^/490. Although I know the exact value (which I found on google to be pi^/490 but I wanted to derive it by myself.

Aidyn Meza 2022-09-20 Answered
Trying to calculate the value of π 4 90 . Although I know the exact value (which I found on google to be π 4 90 ) but I wanted to derive it by myself. While doing so, I arrived at this rather peculiar expression: C = 7 4 720 1 2 P 2
where C is the value of the composite zeta function at 2 and P is the prime zeta function at 2. My question is this. What will be the value of C?
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Answers (1)

Guadalupe Reid
Answered 2022-09-21 Author has 8 answers
Assuming
ζ ( s ) = n 1 n s
P ( s ) = p  prime 1 p s
C ( s ) = n  composite 1 n s
then
C ( s ) = ζ ( s ) P ( s ) 1
and C ( 2 ) = ζ ( 2 ) P ( 2 ) 1 = π 2 6 P ( 2 ) 1 0.192687
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