4.4 $\pi[x]$: Base Prime Counting Function

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The following three plots illustrate the Fourier series for the base prime counting function $\pi[x]$ (blue) evaluated at $f={1, 2, 3}$. The $RiemannR[x]$ function (gray) is shown as a reference.

Fourier Series for p[x] Evaluated at f=1.
$\pi[x]$ evaluated at $f=1$.
Fourier Series for p[x] Evaluated at f=2.
$\pi[x]$ evaluated at $f=2$.
Fourier Series for p[x] Evaluated at f=3.
$\pi[x]$ evaluated at $f=3$.