Here is another Complex problem I can't figure out If f is analytic for │z│≤1 show that ∫D f(x+iy) dx dy = f(0)pi D = {(x,y) : x² + y² ≤ 1} Thanks for the help. Taypez
Last edited by taypez; Dec 18th 2006 at 02:08 PM.
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Originally Posted by taypez Here is another Complex problem I can't figure out If f is analytic for │z│≤1 show that ∫D f(x+iy) dx dy = f(0)pi D = {(x,y) : x² + y² ≤ 1} Thanks for the help. Taypez Let: then: (the change in order of integration is permitted here). So we now need only consider the following integrals: . Now change to polars: . This last term is when and otherwise, which is sufficient to prove the required result: . RonL
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