We Will Use The Following Complex Analysis Result Theorem 0 1 Let U Be An Open Subset Of C And Let N N I Be A Sequen 1 (20.56 KiB) Viewed 123 times
We Will Use The Following Complex Analysis Result Theorem 0 1 Let U Be An Open Subset Of C And Let N N I Be A Sequen 2 (7.95 KiB) Viewed 123 times
We will use the following complex analysis result: Theorem 0.1. Let U be an open subset of C and let {{n}n>i be a sequence of holomorphic functions on U such that i converges uniformly on compact subsets of U. Then II (1 + in) converges uniformly on compact subsets of U. In particular, the limit is a holomorphic function. The n function is defined as (T) = e* II (1 - e2min), for 7 € H. 1 Observe that, by the result quoted above, is a holomorphic function on H. 22
4. Show that n(-1/7)= V-in(). Hint: from the previous exercise n(-1/T) = c/-irn() for some c E C; evaluate at an appro- priate to pin down c.
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