# Generalization of Cauchy's Integral Formula.

Notation: If and , .

Theorem 5.5.1   Take a function analytic in the disk , a positive number such that and a point such that . Then:

where represents the circle whose center is and radius is equal to .

Example 5.5.2   Let (i.e. is the centrer whose center is the origin and whose radius is equal to 2. Then:

Recall that the point 1 is a point interior to .

Example 5.5.3   Let . we wish to compute the following integral:

The two points and are interior to . We decompose the given fraction into simple fractions, by the same method used in Calculus; we have:

hence:

By additivity of the integral, we have:

Noah Dana-Picard 2007-12-24