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

作者：Guo Victor J W^*; Zeng Jiang

来源：Discrete Mathematics, 2008, 308(18): 4069-4078.

DOI：10.1016/j.disc.2007.07.106

• q-binomial coefficient
• q-Chu-Vandermonde formula
• Euler'
• s pentagonal number theorem
• Lucas'
• formulas

Motivated by the resemblance of a multivariate series identity and a finite analogue of Enter';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.

• 出版日期2008-9-28
• 单位华东师范大学