Half-range Fourier series

In mathematics, a half-range Fourier series is a Fourier series defined on an interval [ 0 , L ] {\displaystyle [0,L]} instead of the more common [ − L , L ] {\displaystyle [-L,L]} , with the implication that the analyzed function f ( x ) , x ∈ [ 0 , L ] {\displaystyle f(x),x\in [0,L]} should be extended to [ − L , 0 ] {\displaystyle [-L,0]} as either an even ( f ( − x ) = f ( x ) {\displaystyle f(-x)=f(x)} ) or odd function ( f ( − x ) = − f ( x ) {\displaystyle f(-x)=-f(x)} ). This allows the expansion of the function in a series solely of sines (odd) or cosines (even).

Source: Wikipedia — Half-range Fourier series (CC BY-SA 4.0)

Half-range Fourier series

In mathematics, a half-range Fourier series is a Fourier series defined on an interval [ 0 , L ] {\displaystyle [0,L]} instead of the more common [ − L , L ] {\displaystyle [-L,L]} , with the implication that the analyzed function f ( x ) , x ∈ [ 0 , L ] {\displaystyle f(x),x\in [0,L]} should be extended to [ − L , 0 ] {\displaystyle [-L,0]} as either an even ( f ( − x ) = f ( x ) {\displaystyle f(-x)=f(x)} ) or odd function ( f ( − x ) = − f ( x ) {\displaystyle f(-x)=-f(x)} ). This allows the expansion of the function in a series solely of sines (odd) or cosines (even).

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Source: Wikipedia "Half-range Fourier series" · CC BY-SA 4.0

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