Question

Find fourier series of
F(x) =e ^2x at [-π,π]

Answer 1

Answer:

hope it's correct

Step-by-step explanation:

normalization f^(ω)=∫∞−∞f(t)e−itωdtf^(ω)=∫−∞∞f(t)e−itωdt.

A cute way to to derive the Fourier transform of f(t)=e−t2f(t)=e−t2 is the following trick: Since

f′(t)=−2te−t2=−2tf(t),f′(t)=−2te−t2=−2tf(t),

taking the Fourier transfom of both sides will give us

iωf^(ω)=−2if^′(ω).iωf^(ω)=−2if^′(ω).

Solving this differential equation for f^f^ yields

f^(ω)=Ce−ω2/4f^(ω)=Ce−ω2/4

and plugging in ω=0ω=0 finally gives

C=f