Weierstrass factorization theorem: Difference between revisions

Revision as of 18:40, 4 October 2023

Revision as of 12:10, 8 November 2023

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===Existence of entire function with specified zeroes===

Let <math>\{a_n\}</math> be a sequence of non-zero [[complex numbersnumber]]s such that <math>|a_n|\to\infty</math>.

If <math>\{p_n\}</math> is any sequence of nonnegative integers such that for all <math>r>0</math>,

: <math> \sum_{n=1}^\infty \left( r/|a_n|\right)^{1+p_n} < \infty,</math>