By Raghavan Narasimhan

The unique version of this e-book has been out of print for a few years. The look ance of the current moment variation owes a lot to the initiative of Yves Nievergelt at japanese Washington college, and the aid of Ann Kostant, arithmetic Editor at Birkhauser. because the booklet was once first released, numerous humans have remarked at the absence of routines and expressed the opinion that the ebook may were extra invaluable had routines been incorporated. In 1997, Yves Nievergelt knowledgeable me that, for a decade, he had frequently taught a path at jap Washington in keeping with the ebook, and that he had systematically compiled workouts for his path. He kindly positioned his paintings at my disposal. therefore, the current variation seems in elements. the 1st is largely only a reprint of the unique variation. i've got corrected the misprints of which i've got develop into acutely aware (including these mentioned to me by means of others), and feature made a small variety of different minor alterations.

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**Additional info for Complex Analysis in one Variable**

**Example text**

We have IP(z)1 =rnlao+ a; + ... ;. + lanl) if r is sufficiently large. If P were nowhere 0, we would have IIPE £ (

Proof. Let O

N=k Clearly g(a)=ck#O, so that there is a neighborhood Vc U of a such that g(z)#O for z E V. Clearly then Zf(1 V={a}, so that a is an isolated point of Z f. Corollary. Let Q be a connected open set in