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   Entire function with prescribed values
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   Author  Topic: Entire function with prescribed values  (Read 2339 times)
Tiox
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Entire function with prescribed values  
« on: Nov 27th, 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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Re: Entire function with prescribed values  
« Reply #1 on: Nov 28th, 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 an. Show that
 
[sum] Ang(z)e^(bk(z-ak)) / (z-ak)g'(an)
 
converges for some choice of the constants bn.
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