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      <text>23.2.3.2 Calculation of Fourier coefficients - part 2</text>
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      <text><![CDATA[We summarise these results in the following Key Point:
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<h4>Key Point</h4>
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A function \(f(t)\) with period \(2\pi\) has a Fourier series
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\[ f(t) =  \dfrac{a_0}{2} + \sum_{n=1}^\infty (a_n \cos nt + b_n \sin nt) \]
The Fourier coefficients are
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\[ 
\begin{align}
a_n &amp;= \dfrac{1}{\pi} \displaystyle{ \int _{-\pi}^\pi } f(t) \cos nt \hspace{0.15cm} dt \hspace{1cm} n = 0, 1, 2, \dots \\
b_n &amp;= \dfrac{1}{\pi} \displaystyle{ \int _{-\pi}^\pi } f(t) \sin nt \hspace{0.15cm} dt \hspace{1cm} n = 1, 2, \dots
\end{align}
\]
In the integrals any convenient integration range extending over an interval of \(2\pi\) may be used.
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