无穷级数sum from n=1 to ∞(1/(2n-1)^(2k))的一种计算方法

A Method for Summating the Infinite Series sum from n=1 to ∞(1/(2n-1)^(2k))

根据无穷多项式理论,将余弦函数的幂级数展开式构造成无穷乘积的形式.并且利用ln(1+x)幂级数展开,得到sum from n=1 to ∞(1/(2n-1)～(2k))(k为正整数)的一种计算方法.

Abstract= According to the theory of infinit multinomial, the power series of cosin function was put into the form of infinit product. And a method for calculating the ∞↑∑n=1 1/（2n-1）^2k （k is a positive integer） was obtained by using the power series expansion ln（1＋x）