On singularities of generating functions of Pólya frequency sequences of finite order (Q5928181)
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scientific article; zbMATH DE number 1582156
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On singularities of generating functions of Pólya frequency sequences of finite order |
scientific article; zbMATH DE number 1582156 |
Statements
On singularities of generating functions of Pólya frequency sequences of finite order (English)
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2 October 2001
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``Let \(E\) be a closed set in \(\mathbb{C}\) satisfying the conditions: (i) \(E\) is symmetric with respect to the real axis, (ii) \(E\cap\{z:|z|\leq 1\}= \phi\). For any \(r\geq 1\) there exists a function \(f(z)\) satisfying the properties: (i) \(f(z)\) is a generating function of a Pólya frequency sequence of order \(r\), (ii) the singularity set of \(f(z)\) is \(E\cup \{1\}\).
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generating function
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Pólya frequency sequence
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singularity
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