Complex analysis jn sharma pdf

The same idea can be used to analyze functions of two (or more) complex variables

First a de nition: we say f(z; t) is analytic on C2 if it is analytic in each variable separately

This implies that f is locally given by a convergent power series P aij(z z0)i(w w0)j

In other words, J( ) is a complex number which depends only on the isomorphism class of E = C=(Z Z ); we have J( 1) = J( 2) i E1 = E2; and every complex number arises as J( ) for some

Preface Complex analysis is a branch of mathematics that involves functions of complex numbers

It provides an extremely powerful tool with an unex- pectedly large number of applications, including in number theory, applied mathematics, physics, hydrodynamics, thermodynamics, and electrical en- gineering