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Topic: Entire function with prescribed values (Read 2339 times) 

Tiox
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Entire function with prescribed values
« on: Nov 27^{th}, 2005, 10:49pm » 
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Please help me out on this problem: Prove that if a_n are complex numbers such that a_n tends to infinity, and A_n are arbitrary complex numbers, then there exists an entire function F which satisfies F(a_n) = A_n.


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Icarus
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Re: Entire function with prescribed values
« Reply #1 on: Nov 28^{th}, 2005, 8:04pm » 
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When Ahlfors's Complex Analysis gives this problem, he also gives the following hint: Let g be an entire function having simple zeros at all the a_{n}. Show that [sum] A_{n}g(z)e^(b_{k}(za_{k})) / (za_{k})g'(a_{n}) converges for some choice of the constants b_{n}.


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"Pi goes on and on and on ... And e is just as cursed. I wonder: Which is larger When their digits are reversed? "  Anonymous



