An inequality and its application to Mahler's partition function (Q1313447)
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scientific article; zbMATH DE number 492582
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An inequality and its application to Mahler's partition function |
scientific article; zbMATH DE number 492582 |
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An inequality and its application to Mahler's partition function (English)
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16 May 1994
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The author gives a short proof (in fact a refinement) of M. Lewin's inequality \[ \sum^ n_{i=0,i+j=n} t^{ij+i-j}/i!j!< \sum^ n_{i=0,i+j=n} t^{ij+1}/i!j!, \] where \(t>1\) is a real number, and \(n>0\) a positive integer. An interesting corollary is also given. This inequality occurs in the theory of partitions of positive integers.
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Mahler's partition function
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inequalities for sums
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logarithmically convex functions
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Lewin's inequality
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partitions of positive integers
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