逐项微分

讨论了Jacobi级数的逐项微分，应用它，推广了Jacobi级数部分和逼近的已知结果且在某些情况下作了改进。

We discuss term by term differentiation of the Jacobi series , based on it a known theorem concerning approximation by the partial sums of Jacobi series is extended and in a special case itis improved .

用逐项微分法求随机变量的数学期望与方差

To Get the Digital Expectation and Variance of Random Variance by the Method of Termwise Differentiation

利用无穷级数可以将一些复杂的代数函数和超越函数展成简单形式，然后对其进行逐项微分或积分，进而对这些函数处理起来得心应手。

It makes a lot of complex algebraic functions and excessive functions become simple , and then we can differentiate or integrate term by term . Therefore , these functions can be done with easily .

该方法运用逐项微分法将幂级数的收敛和函数转化为相应的常系数线性微分方程，求出微分方程的通解从而得到相应常数项级数之和。

A differential equation with constant coefficient is obtained by Termwise differentiation on the sum function of power series in this method , and the sum of constant series is able to be solved from the general solution of differential equation .