Question

我目前正在尝试计算函数x ^（1/2）的泰勒级数之和（这就是它在Wolfram中的表现：http://www.wolframalpha.com/input/?i=taylor+series+x%5E%281%2F2%29）这是所需的公式：http://i.imgur.com/YvVOQIR.png

我无法计算二项式系数。我将它分为两部分（分母中的分子和阶乘）。分子总是计算为0值（除了通过初始化应该为1的一次）。

编辑：将int更改为双精度（此处也更新了代码）并且运行良好并编辑了代码：

    #include <iostream>
#include <stdio.h> 
#include <math.h>

using namespace std;


double x;
double e;



void taylor() // taylor series
{

double result = 0;
double previous = 1;

for(double n=0; abs(previous-result) > e;n++) //cycle for caltucalting to given precision
    {
double binomial=1; // variable for binomial coef
double fact=1; //variable for factorial
double topbin=1; //variable for top part of binomial coef

        previous=result;
        for(double k=1;k<=n;k++)        
            {   
                fact *= k;            //calcucating factorial
                topbin *= ((1.0/2.0)-k+1); //calculating top part of binomial coef
            }

        binomial=double(topbin)/double(fact);        //calculating whole binomial coef
        result+=binomial*(pow((-1+x),n)); // calculating taylor series

        cout<<"topbin "<<topbin<<endl;
        cout<<"fact "<<fact<<endl;
        cout<<"binomial "<<binomial<<endl;
        cout<<"taylor sum on "<<n<<" iteration: "<<result<<endl;
        cout<<endl;
    }
cout<<"taylor sum:"<<result<<endl;
}

void main()
{
cout<<"Enter x"<<endl;
cin>>x;
cout<<"Enter e"<<endl;
cin>>e;
taylor();
double y=1/sqrt(pow(x,2)-1);
cout<<"y= "<<y<<endl;

}

计算泰勒函数x ^（1/2）的和

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