JP Journal of Algebra, Number Theory and Applications
Volume 10, Issue 2, Pages 185 - 191
(April 2008)
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A FORMULA FOR THE SUM OF THREE TRIANGULAR NUMBERS AND SOME EXPLORATIONS
Alexander Eric Patkowski (U. S. A.)
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Abstract: Our goal is to establish a new generating function for the sum of three triangular numbers. The new generating function may be viewed as a companion to the sum of three squares formula offered in [3]. In addition to our alternative proof, we explore some examples that may be deduced from identities given in Fine’s text. |
Keywords and phrases: q-series, theta
functions, triangular numbers. |
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