\(E\Upsilon PHKA\)! \(\mathrm{num}=\Delta +\Delta +\Delta\) (Q1071795)
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scientific article; zbMATH DE number 3939417
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(E\Upsilon PHKA\)! \(\mathrm{num}=\Delta +\Delta +\Delta\) |
scientific article; zbMATH DE number 3939417 |
Statements
\(E\Upsilon PHKA\)! \(\mathrm{num}=\Delta +\Delta +\Delta\) (English)
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1986
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The author uses Bailey transforms and some standard identities for basic hypergeometric series to prove that the cube of \(1+x+x^3+x^6+x^{10}+\ldots\) is a series all of whose coefficients are strictly positive. This implies Gauss' result that every positive integer can be expressed as the sum of three triangular numbers
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generating function
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number of representations
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Bailey transforms
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sum of three triangular numbers
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