两类含参变量Dirichlet积分的公式解

Formula solutions for two kinds of Dirichlet’s integral with one variable

给出了含参变量Dirichlet积分In,m(s)的定义。数学分析中的许多含参变量积分都是In,m(s)的特例。利用三角降次公式及解析函数的理论解决了含参变量Dirichlet积分的公式解问题,由此推出第一类Dirichlet积分与第二类Dirichlet积分的公式解。通过计算,解决了In,m(s)的表示问题。

The definition of Dirichlet’s integral I_(n,m)(s) with one variable has been given.Many integrals with variables in mathematic analysis are special cases of I_(n,m)(s). Using trigonometric power reduction formulas and analytic function theory, the Dirichlet’s integral I_(n,m)(s) has been solved,with name of formula solutions.From that, the first kind and second kind Dirichlet’s integrals have been presented by computation of I_(n,m)(s).