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

Abstract:

      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.