Why is 2L Used for Function Periods?

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SUMMARY

The use of 2L as the period of a function in mathematics literature is primarily due to its relationship with the heat equation and the symmetry it provides when considering a rod of length 2L with endpoints at ±L. This choice enhances clarity in mathematical expressions, particularly in the context of sine and cosine functions, which have a natural period of 2π. The formulation of Fourier coefficients becomes more straightforward when using 2L, as it simplifies the notation from 2nπx/D to nπx/L, making it easier to remember and apply.

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Why do most mathematics literature use 2L for the period of a function? Is it related to heat equation with a rod of length L?
 
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matqkks said:
Why do most mathematics literature use 2L for the period of a function? Is it related to heat equation with a rod of length L?

Having a rod of length 2L with ends at [itex]\pm L[/itex] instead of a rod of length D with ends at 0 and D makes the mid-point symmetry more obvious.

Also the period of the sine and cosine functions is [itex]2\pi[/itex] and [itex]\frac{2n\pi x}{2L} = \frac{n\pi x}{L}[/itex] is neater than [itex]\frac{2n\pi x}{D}[/itex].
 
It may be as simple as noting for a general period, instead of ##2\pi## call it ##2p##. It certainly makes the Fourier coefficient formulas easier to remember. And it's why I like to use ##p## instead of ##L## in such formulas.
 
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