Lacunary function
January 8th, 2008 by WaltWikipedia has an interesting page on lacunary series, which are Taylor series or Fourier series with sparse coefficients. Lacunary series can be used to give examples of phenomena such as a complex analytic function which has essential singularities at every point of the unit circle, or a function whose Fourier series diverges almost everywhere.
January 9th, 2008 at 12:55 pm
Surely, you meant every point on the unit circle, not disk?
January 9th, 2008 at 1:20 pm
You’re right! I fixed it.