【摘要】 利用发生函数和矩阵方法,研究了一个特殊的二项式系数[n+λ n-k]和它所构成的矩阵.得到以[n+λ n-k]为矩阵元素的Pascal型矩阵的指数分解和乘积分解公式.同时,考察了与二项式型多项式相伴的函数矩阵Pn,λ[x]及其性质.更多还原

【Abstract】 The special binomial coefficient [ n+λ n-k ] and its related matrices are investigated. The factorization and exponential expansion of (n+1)×(n+1) Pascal type matrix Pn,λ associated with [ n+λ n-k ] are obtained by using generating function and matrix method. Furthermore, the functional matrix Pn,λ[x] with polynomial of binomial type related to [ n+λ n-k ] and its properties are studied.更多还原