Multiple extensions of a finite Euler's pentagonal number theorem and the Lucas formulas |
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| Authors: | Victor JW Guo Jiang Zeng |
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| Institution: | a Department of Mathematics, East China Normal University, Shanghai 200062, People's Republic of China
b Institut Camille Jordan, Université de Lyon, Université Lyon 1, UMR 5208 du CNR, 43, boulevard du 11 novembre 1918, F-69622 Villeurbanne Cedex, France |
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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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| Keywords: | 05A10 05A30 |
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