Find the Fourier integral representation of the function f(x) = {1x1₁ |x < π |x > T

Q: [6] Find the Fourier integral representation of f(x) = { 02 0 1.

A: Fourier integral representation

Q: Part c: Consider the function f : [-1, 1] → R { -1 = S', f(x)g(x).

A:

Q: 25. Find the harmonic conjugate of u = In|z| and corresponding analytic function f (z) = u + iv.

A:

Q: Show also that the function ln(z) is unique up to addition of a constant 2πik, k ∈ Z.

A: ln(mn) =ln(m) +ln(n)  ln(am) =mln(a)

Q: 4) For the following function f(x), find the exponential Fourier transform of f(x) as a Fourier…

A:

Q: Let f. [-1/2,1/2] → R be given by f(x) = cos (x) * exp(x). There exists a unique inverse function g:…

A: We will use of chain rule