Recent content by Risborg

  1. R

    Power series where radius of convergence > lower limit

    Okay thank you so much for the help. I think I found a solution by choosing ##a_n = 2## if ##n## is even and ##a_n = 3## if ##n## is odd, then I end up having ##\tilde{R} = \frac{2}{3} < 1 = R##.
  2. R

    Power series where radius of convergence > lower limit

    Oops I forgot to change the variables when I copied from a latex example, it should be fixed now.
  3. R

    Power series where radius of convergence > lower limit

    Homework Statement Let ##\sum^{\infty}_{n=0} a_n(z-a)^n## be a real or complex power series and set ##\alpha = \limsup\limits_{n\rightarrow\infty} |a_n|^{\frac{1}{n}}##. If ##\alpha = \infty## then the convergence radius ##R=0##, else ##R## is given by ##R = \frac{1}{\alpha}##, where...
  4. R

    Integration test of dirac delta function as a Fourier integral

    Homework Statement Problem: a) Find the Fourier transform of the Dirac delta function: δ(x) b) Transform back to real space, and plot the result, using a varying number of Fourier components (waves). c) test by integration, that the delta function represented by a Fourier integral integrates...