Legendre多项式

时间限制: 1 Sec  内存限制: 128 MB

题目描述

Legendre多项式的递归公式

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" alt="" width="567" height="171" />

编写程序, 输出n阶Legendre多项式x在[-1,1]闭区间的101个点值, (每个点等间距)

输入

输入阶数 n

输出

输出n阶Legendre多项式x在[-1,1]闭区间的101个点值, 保留4位有效小数(每个点等间距)

样例输入

5

样例输出

-1.0000
-0.7204
-0.4796
-0.2744
-0.1017
0.0411
0.1570
0.2484
0.3177
0.3674
0.3995
0.4162
0.4193
0.4107
0.3922
0.3652
0.3313
0.2919
0.2482
0.2014
0.1526
0.1028
0.0529
0.0037
-0.0441
-0.0898
-0.1330
-0.1730
-0.2095
-0.2421
-0.2706
-0.2948
-0.3144
-0.3294
-0.3397
-0.3454
-0.3465
-0.3431
-0.3353
-0.3234
-0.3075
-0.2880
-0.2650
-0.2389
-0.2101
-0.1788
-0.1455
-0.1106
-0.0744
-0.0374
0.0000
0.0374
0.0744
0.1106
0.1455
0.1788
0.2101
0.2389
0.2650
0.2880
0.3075
0.3234
0.3353
0.3431
0.3465
0.3454
0.3397
0.3294
0.3144
0.2948
0.2706
0.2421
0.2095
0.1730
0.1330
0.0898
0.0441
-0.0037
-0.0529
-0.1028
-0.1526
-0.2014
-0.2482
-0.2919
-0.3313
-0.3652
-0.3922
-0.4107
-0.4193
-0.4162
-0.3995
-0.3674
-0.3177
-0.2484
-0.1570
-0.0411
0.1017
0.2744
0.4796
0.7204
1.0000

提示

x的取值在[-1, 1]之间, 每个点之间相距0.02, 即x=x+0.02, 这样就有101个点的数据

 #include <iostream>
#include <stdio.h>
using namespace std; double Leg(int n, double x)
{
double ans;
if(n == )
ans = ;
else if(n == )
ans = x;
else ans = ( ( * n - ) * x * Leg(n-,x) - (n - ) * Leg(n - ,x) ) / n;
return ans;
} int main()
{
int n;
double x;
scanf("%d",&n);
for(x = -; x <= 1.02; x=x+0.02)
{
double leg;
leg = Leg(n,x);
printf("%.4lf\n",leg);
}
return ;
}

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