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A Property of the Zeros of the Successive Derivatives of Integral Functions


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1 Madras University, India
     

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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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  • A Property of the Zeros of the Successive Derivatives of Integral Functions

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Authors

V. Ganapathy Iyer
Madras University, India

Abstract


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.