q超几何级数 2Φ0[a,b;z]的两个基本恒等式及其一些应用

Two Identities for q-Hypergeometric Series 2Φ0 and Its Applications

中文关键词:  q超几何级数  矩阵方程  特殊矩阵

英文关键词:q-hypergeometric series  matrix equation  special matrices.

中文摘要:

      本文由有限域上交错矩阵方程ＸＫ_２υＸ′＝０的解数公式得到ｑ超几何级数 ₂Φ₀的一个基本恒等式，并且用它能直接把一些特殊矩阵的这类方程的解数由函数 ₂Φ₀表出．另外还用 ₂Φ₀的一个恒等式得出Ｆ_q上ｍ阶特殊矩阵的个数．

英文摘要:

      In this paper, an elementary identity for q-hypergeometric series ₂Φ₀ is obtained from two formulas of the number of solutions to the alternate equation XK_2υ X′=0 . Using this identity, formulas of the number of solutions of some special matrix equations are represented by q-hypergeometric series. Finally, using another identity of ₂Φ₀, the numbers of some special matrices over F_q are also obtained.