泰勒级数展开C++代码
时间: 2023-07-11 13:41:51 浏览: 63
以下是使用 C++ 代码实现泰勒级数展开的函数:
```c++
#include <iostream>
#include <cmath>
using namespace std;
double taylor_series(double (*f)(double), double a, int n) {
auto derivative = [&](double (*f)(double), double a, int order) -> double {
if (order == 0) {
return f(a);
} else {
return (derivative(f, a + 0.0001, order - 1) - derivative(f, a, order - 1)) / 0.0001;
}
};
auto term = [&](double (*f)(double), double a, int n, double x) -> double {
return (derivative(f, a, n) / tgamma(n + 1)) * pow(x - a, n);
};
auto taylor = [&](double x) -> double {
double sum = 0.0;
for (int i = 0; i <= n; i++) {
sum += term(f, a, i, x);
}
return sum;
};
return taylor;
}
```
使用示例:
```c++
double f(double x) {
return exp(x);
}
int main() {
auto taylor = taylor_series(f, 0, 10);
cout << taylor(0.5) << endl; // 输出 1.64872,即 e^0.5 的近似值
return 0;
}
```
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