Is it possible to find a analytic function having zeros at 1/n?

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Is it possible to find a analytic function having zeros at 1/n?

2006-06-30 22:58:00 · 2 answers · asked by sarkar_sumitra_bir 1 in Science & Mathematics ➔ Mathematics

2 answers

lim 1/n when n->0 = ∞

2006-06-30 23:03:53 · answer #1 · answered by ice cream with chocolate 6 · 0⤊ 0⤋

If the function is to be analytic everywhere, with zeros only at 1/n (for all natural numbers n?), then no. Because of continuity, it would have to have a zero at 0 also.

If the function need only be analytic on, say, the open interval (0,1), then yes. for example f(x)=sin(pi/x).

2006-07-01 08:43:05 · answer #2 · answered by Anonymous · 0⤊ 0⤋