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arXiv · 0707.4328

Multiple extensions of a finite Euler's pentagonal number theorem and the Lucas formulas

Victor J. W. Guo·Jiang Zeng
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Abstract

Motivated by the resemblance of a multivariate series identity and a finite analogue of Euler's pentagonal number theorem, we study multiple extensions of the latter formula. In a different direction we derive a common extension of this multivariate series identity and two formulas of Lucas. Finally we give a combinatorial proof of Lucas' formulas.

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Victor J. W. Guo, Jiang Zeng. 2007-07-30. Multiple extensions of a finite Euler's pentagonal number theorem and the Lucas formulas. https://doi.org/10.1016/j.disc.2007.07.106

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