Find all functions $f$ analytic in the open unit disk and such that $$f(\frac{1}{n})= e^{-n} $$ I don't know how to start
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See also https://math.stackexchange.com/questions/1287448/if-f-is-analytic-and-f1-n-e-n-for-all-n-0-why-is-fz-0-fo and https://math.stackexchange.com/questions/1701284/show-that-there-does-not-exist-any-analytic-function-for-which-f-left-dfrac1 – Chris Culter Jul 07 '20 at 04:36
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And https://math.stackexchange.com/questions/1185504/does-there-exist-an-analytic-function-s-t-f-left-frac1n-right-2-n – Chris Culter Jul 07 '20 at 04:38
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Can anyone tell, what kind of singularity the function have? – A learner Jul 07 '20 at 04:55