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.