Definition:Fourier Series/Also defined as

Fourier Series: Also defined as

The form of the Fourier series given here is more general than that usually given.

The usual form is one of the cases where $\alpha = 0$ or $\alpha = -\pi$, thus giving a range of integration of either $\openint 0 {2 \pi}$ or $\openint {-\pi} \pi$.

The actual range may often be chosen for convenience of analysis.

Sources

• 1961: I.N. Sneddon: Fourier Series ... (previous) ... (next): Chapter One: $\S 2$. Fourier Series: $(6)$
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Fourier series
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Fourier series
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Fourier series
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Fourier series