Illustrations of Fourier Series Derived via Methods 2 and 3

I’ve defined three methods for derivation of Fourier series for prime counting functions. This website initially focused on illustrating the Fourier series for prime counting functions derived via the initial method 1, but I’m now in the process of adding illustrations for Fourier series derived via methods 2 and 3. Pages 4 and 5 summarize the number of formulas I’ve derived for the base prime counting functions and their first-order derivatives respectively. Page 4.10 will illustrate three formulas for Riemann’s prime-power counting function $J[x]$, and page 4.11 will illustrate six formulas for the second Chebyshev function $\psi[x]$. Page 5.10 will illustrate six formulas for the first-order derivative $J'[x]$ of Riemann’s prime-power counting function, and page 5.11 will illustrate six formulas for the first-order derivative $\psi'[x]$ of the second Chebyshev function.