【摘要】 行列式计算有许多方法，其中针对含参数的行列式时常需要进行分类讨论.给出右上角元素为α、左下角元素为β、主对角线上元素分别x₁,x₂,…,x_n的一类特殊行列式的多种算法，包括数学归纳法、拆分法、升阶法、按行（列）展开后迭代法和按行（列）展开后直接计算法，从中得到这类行列式的一个具有一般性的公式.所采用的多种方法不但去掉了文献中基于两种不同情况进行分类计算的限制，而且得到的一般性公式，还统一了已知算法在两种分类情况下的不同结果，这对所考虑的行列式计算而言是新尝试.更多还原

【Abstract】 There are many methods to calculate determinants, among which the determinants with parameters often need to be classified and discussed.This paper presents several algorithms for a class of special determinants with upper right corner element being α,lower left corner element being β,and elements on the main diagonal being x₁,x₂,…,x_n,respectively, including mathematical induction method, splitting method, raising order method, iterative method after expanding by rows（columns）,and direct calculation method after expanding by rows（columns）.As a result, a general formula for the class of determinant is obtained.These methods used in this article not only remove the limitation of classification calculation based on two different situations in the literature, but also unify the different results of known algorithm in two classification situations, which is a new attempt for the determinant calculation under consideration.更多还原