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Tiox
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 Entire function with prescribed values   « on: Nov 27th, 2005, 10:49pm » Quote Modify Remove

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 » Quote Modify

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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