- Theorem 1
Where denotes a product over the primes.
One will notice that every other term has been removed. It then follows that,
One may notice that this process sieves the RHS, meaning that,
It therefore follows that,
- Theorem 2
Multiplying the integrand through ,
Writing as a power series,
Using the substitution
Using properties of infinite series',
By the definition of the function,
Which is true by definition.