数学杂志
數學雜誌
수학잡지
JOURNAL OF MATHEMATICS
2007年
2期
135-140
,共6页
二项式系数%二项式型多项式%Pascal矩阵
二項式繫數%二項式型多項式%Pascal矩陣
이항식계수%이항식형다항식%Pascal구진
binomial coefficient%polynomial of binomial type Pascal matrix
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-к)和它所构成的矩阵.得到以(n+λ)/(n-к)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P(n,λ)[x]及其性质.
利用髮生函數和矩陣方法,研究瞭一箇特殊的二項式繫數(n+λ)/(n-к)和它所構成的矩陣.得到以(n+λ)/(n-к)為矩陣元素的Pascal型矩陣的指數分解和乘積分解公式.同時,攷察瞭與二項式型多項式相伴的函數矩陣P(n,λ)[x]及其性質.
이용발생함수화구진방법,연구료일개특수적이항식계수(n+λ)/(n-к)화타소구성적구진.득도이(n+λ)/(n-к)위구진원소적Pascal형구진적지수분해화승적분해공식.동시,고찰료여이항식형다항식상반적함수구진P(n,λ)[x]급기성질.
The speciat binomial coefficient (n+λ)/(n-к) and its related matrices are investigate The faetorization and exponential expansion of (n+1)X(n+1) Pascal type matrix P(n,λ)associated with(n+λ)/(n-к) are obtainea by using generating function and matrix method.Furthermore,the functional matrix P(n,λ)[x] with polynomial of binomial type related to (n+λ)/(n-к)and its properties are studied.
