Definition


An Analytic (Complex Analysis) function has a singularity if it is not analytic at that point . (undefined, discontinuity, non-differentiable, …)

Examples


  • is not differentiable at .
  • is undefined at .
  • is not continuous at any .

Classification of Singularities


  1. Removable Singularity
  2. Isolated Singularity/Pole
  3. Essential Singularity
  4. Non-isolated Singularity