Post by Admin on Jul 3, 2017 6:46:10 GMT
Gary
When I read the first paragraph on page 414 about Morera's theorem I thought that there was a contradiction with functions like $f(z)=(1/z^2), (1/z^3)$ etc., because according to section IX on Power functions $\oint_{\gamma}f(z)dz$ vanishes for any $\gamma$ which encloses the origin (a pole). Then I realised that for Morera's Theorem to hold the loop integral must vanish for all loops, and it certainly will not vanish if the loop passes through the origin, and so the theorem does not hold for these functions unless the origin is excluded. Huge sigh of relief - it all makes sense!
Vasco
When I read the first paragraph on page 414 about Morera's theorem I thought that there was a contradiction with functions like $f(z)=(1/z^2), (1/z^3)$ etc., because according to section IX on Power functions $\oint_{\gamma}f(z)dz$ vanishes for any $\gamma$ which encloses the origin (a pole). Then I realised that for Morera's Theorem to hold the loop integral must vanish for all loops, and it certainly will not vanish if the loop passes through the origin, and so the theorem does not hold for these functions unless the origin is excluded. Huge sigh of relief - it all makes sense!
Vasco
