5.6 $K_b'[x]$: First-Order Derivative of Simple Prime-Power Counting Function

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The Fourier series for the first-order derivative $K_b'[x]$ of the simple prime-power counting function evaluates to $2\ f$ at prime powers where $f$ is the evaluation frequency limit.


First-Order Derivative of Simple Prime-Power Counting Function (i.e. k'[x]) Evaluated at f=1.
$K_b'[x]$ evaluated at $f=1$.

First-Order Derivative of Simple Prime-Power Counting Function (i.e. k'[x]) Evaluated at f=1.
$K_b'[x]$ evaluated at $f=1$.
First-Order Derivative of Simple Prime-Power Counting Function (i.e. k'[x]) Evaluated at f=2.
$K_b'[x]$ evaluated at $f=2$.
First-Order Derivative of Simple Prime-Power Counting Function (i.e. k'[x]) Evaluated at f=3.
$K_b'[x]$ evaluated at $f=3$.


First-Order Derivative of Simple Prime-Power Counting Function (i.e. k'[x]) around x=19 Evaluated at f={2, 4, 8}.
$K_b'[x]$ around $x=19$ evaluated at $f={2, 4, 8}$.