If I remember correctly you can get even a stronger result. Let a_n, b_n and c_n be sequences of complex numbers and i_n be a sequence of natural numbers. Then I believe there exists a meromorphic functions function that is takes the value b_n on a_n for all n, and has a pole of order i_n at c_n for all n. Assuming that the a_n and c_n are disjoint and have no accumulation point. It's been a while since I thought about complex analysis but I seem to remember learning this.
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If I remember correctly you can get even a stronger result. Let a_n, b_n and c_n be sequences of complex numbers and i_n be a sequence of natural numbers. Then I believe there exists a meromorphic functions that is takes the value b_n on a_n for all n, and has a pole of order i_n at c_n for all n. Assuming that the a_n and c_n are disjoint and have no accumulation point. It's been a while since I thought about complex analysis but I seem to remember learning this. |
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