When zeros at natural numbers implies zero everywhere

Suppose a function f(z) equals 0 at z = 0, 1, 2, 3, …. Under what circumstances might you be able to conclude that f is zero everywhere? Clearly you need some hypothesis on f. For example, the function sin(πz) is zero at every integer but certainly not constantly zero. Carlson’s theorem says that if […] The post When zeros at natural numbers implies zero everywhere first appeared on John D. Cook....

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