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Question: fractional Fourier transform

Question:fractional Fourier transform

mehdi jafari 764 Maple
fourier-transform
April 10 2023
1

Hi, i want to calculate fourier transform of functions with fractional powers. how can i do this? for example what is fourier transform of sqrt(x) ? I want a function or an expression as output, not the inetgral itself. thnx in advance

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restart:with(inttrans):
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f := x -> x^(1/2);
int(f(x)*exp(-I*w*x), x = -infinity .. infinity);

proc (x) options operator, arrow; x^(1/2) end proc

  

int(x^(1/2)*exp(-I*w*x), x = -infinity .. infinity)

 (1)
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fourier(f(x),x,w)

fourier(x^(1/2), x, w)

 (2)
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