- #1

- 79

- 1

## Main Question or Discussion Point

Is there any way to calculate the Fourier transform of the functions

[tex] \frac{d\pi}{dx}-1/log(x) [/tex] and [tex] \frac{d\Psi}{dx}-1 [/tex]

(both are understood in the sense of distributions)

i believe that these integrals (even with singularities) exist either in Cauchy P.V or Hadamard finite part sense but if possble i would need a help, thanks

EDIT:= 'pi(x)' here is the prime counting function and 'Psi (x) ' is the Tchebycheff function.

[tex] \frac{d\pi}{dx}-1/log(x) [/tex] and [tex] \frac{d\Psi}{dx}-1 [/tex]

(both are understood in the sense of distributions)

i believe that these integrals (even with singularities) exist either in Cauchy P.V or Hadamard finite part sense but if possble i would need a help, thanks

EDIT:= 'pi(x)' here is the prime counting function and 'Psi (x) ' is the Tchebycheff function.