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Displaying similar documents to “On approximation and interpolation of entire functions with index-pair (p,q).”

The deficiency of entire functions with Fejér gaps

Takafumi Murai (1983)

Annales de l'institut Fourier

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We say that an entire function f ( z ) = k = 0 a k z n k ( 0 = n 0 < n 1 < n 2 < ... ) has Fejér gaps if k = 1 1 / n k < . The main result of this paper is as follows: An entire function with Fejér gaps has no finite deficient value.

On the uniqueness of an entire function sharing a small entire function with some linear differential polynomial

Xiao-Min Li, Hong-Xun Yi (2009)

Czechoslovak Mathematical Journal

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We prove a theorem on the growth of nonconstant solutions of a linear differential equation. From this we obtain some uniqueness theorems concerning that a nonconstant entire function and its linear differential polynomial share a small entire function. The results in this paper improve many known results. Some examples are provided to show that the results in this paper are the best possible.