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Topic: Entire function with prescribed values (Read 2610 times) |
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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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Icarus
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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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