The trigonometric Fourier series of an even function of time does not have

where $a_0$ is the constant term, $a_n$ and $b_n$ are the coefficients of the cosine and sine terms, respectively, and $\omega$ is the angular frequency.

The constant term, $a_0$, is present in the Fourier series of any function, even or odd. The cosine terms, $a_n \cos(n \omega x)$, are present in the Fourier series of an even function if $n$ is even, and the sine terms, $b_n \sin(n \omega x)$, are present in the Fourier series of an even function if $n$ is odd.

Therefore, the Fourier series of an even function of time does not have odd harmonic terms.