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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.

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

Fourier Series for Prime Counting Functions

The primary purpose of this website is the illustration of the genuine natural Fourier series for prime counting functions.

**Navigation Links: – Next Page – Parent Page**

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.