2019-03-15
Some Formulas of Liouville in the Spirit of Gauss
Publication
Publication
Summary.: We show how Liouville’s formulas for the number of representations of a positive integer by the forms (Formula presented.), and (Formula presented.) follow in a simple systematic way from a beautiful identity of Jacobi using some elementary relationships between the infinite series P(x) = 1 + 2x + 2x 4 + 2x 9 + ... and Q(x) = 1 − 2x + 2x 4 + 2x 9 + ... given by Gauss.
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| Persistent URL | dx.doi.org/10.1080/0025570X.2019.1543989 |
| Journal | Mathematics Magazine |
| Citation |
Williams, K.S. (2019). Some Formulas of Liouville in the Spirit of Gauss. Mathematics Magazine, 92(2), 83–90. doi:10.1080/0025570X.2019.1543989
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