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A Property of the Zeros of the Successive Derivatives of Integral Functions
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The following result has been proved by Takenaka:
THEOREM 1. Let f(z) be an integral function of order one and type not exceeding σ. Let [αn] be a sequence such that
lim |αn|=L<log2. (1)
Let f(n)(αn)=0, n=0, 1, 2 . . .[f(0)(z)=f(z)]. Then f(z)=0.
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