4.7 $\vartheta[x]$: First Chebyshev Function

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The following three plots illustrate the Fourier series for the first Chebyshev function $\vartheta[x]$ (blue) evaluated at $f={1, 2, 3}$. The linear function $x$ (gray) is shown as a reference.

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