eljose79
Mar18-03, 04:03 AM
let be the function a(x) defined as:
1 Iff x is prime
0 x is not prime
then appliying Abel,s summation formula.it would be
S(p)f(p)= c+I(0,Infinite)Pi(x)f´(x)
where f(x) is a differentiable function and S(p) means summ over all the primes....Pi(x) is the usual formula of a number of primes <or = x.....żis this formula true?.
b)I think i have discovered a formula to summ all primes by using euler,s transformation to summ alternate series .
in fact if you take the serie with general term:
(-1)**n(Pi(n)-Pi(n-1))f(n) and apply Euler,s transformation you can find and approach to the summ of the series above and this series is equal to:
S(0,Infinite)(-1)**nf(n)+S(p)f(n) .
So you can obtain an approach to S(p)f(n).....
1 Iff x is prime
0 x is not prime
then appliying Abel,s summation formula.it would be
S(p)f(p)= c+I(0,Infinite)Pi(x)f´(x)
where f(x) is a differentiable function and S(p) means summ over all the primes....Pi(x) is the usual formula of a number of primes <or = x.....żis this formula true?.
b)I think i have discovered a formula to summ all primes by using euler,s transformation to summ alternate series .
in fact if you take the serie with general term:
(-1)**n(Pi(n)-Pi(n-1))f(n) and apply Euler,s transformation you can find and approach to the summ of the series above and this series is equal to:
S(0,Infinite)(-1)**nf(n)+S(p)f(n) .
So you can obtain an approach to S(p)f(n).....