K.S. Narain , ICTP
lecture 10
The Converse of the Cauchy theorem, Cauchy Criteria for Convergence,Geometric series
- If we know that there is a continuous function whose integral over any closed contour in some region vanishes then that function is analytic in that region.
- Then we showed that if f is continuous for contour C(C is a closed
- contour in some region R) then f(z) is analytic and in fact we proved it.
- We prove Cauchy Criteria for Convergence and talk about uniform
- Convergence and give some examples.
- Necessary conditions for convergent series are provided
- We give some examples of convergency like geometric series we also prove it.