Algebraic independence of solutions of first-order rational difference equations (Q384014)
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scientific article; zbMATH DE number 6232382
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Algebraic independence of solutions of first-order rational difference equations |
scientific article; zbMATH DE number 6232382 |
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Algebraic independence of solutions of first-order rational difference equations (English)
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25 November 2013
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The author gives a new proof of the algebraic independence of the functions \(x\), \(e^x\) and the Weierstraß\ function \(\mathfrak{P}(x)\) by using the functional relation which allows one to express \(\mathfrak{P}(2x)\) as a rational function of \(\mathfrak{P}(x)\). This is a particular case of a general result involving solutions of first-order nonlinear difference equations. Other applications of this general result are given.
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first-order rational difference equation: algebraic independence
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solvability
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reducibility
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0.7652393579483032
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0.7563583850860596
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0.7561798095703125
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