beta(),betaf()和betal()是C++ STL中的内置函数,用于计算两个正实数值的beta函数。该函数将两个变量x和y作为输入,并返回x和y的beta函数。 x和y的Beta函数(也称为第一类Euler积分)可以定义为:

用法

double beta(double x, double y)or long double betal(long double x, long double y)or float betaf(float x, float y)

参数:该函数接受两个强制性参数x和y,它们指定浮点或整数类型的值。参数可以是double,double或float,float或long double,long double数据类型。

返回值:该函数返回x和y的beta函数的值。返回类型取决于传递的参数。与参数相同。

注意:该函数在C++ 17(7.1)及更高版本中运行。

以下示例程序旨在说明beta(),betaf()和betal()函数:

// C++ program to illustrate the three functions // Being a special function, beta is only guaranteed // to be in cmath if the user defines //  __STDCPP_WANT_MATH_SPEC_FUNCS__ before including // any standard library headers. #define __STDCPP_WANT_MATH_SPEC_FUNCS__ 1 #include <bits/stdc++.h> using namespace std;   int main() {     // Computes the beta function of 5 and 4 and print it     // If provided arguments are not of type double     // they are implicitly type-casted to the higher type.       // first example of beta()     cout << beta(5, 4) << "\n";       // second example of betaf()     cout << betaf(10.0, 4.0) << "\n";       // third example of betal()     cout << betal(10.0, 6.7) << "\n";     return 0; }

输出:

0.003571430.000349651.65804e-005

Beta函数的应用:用于计算二项式系数。以beta函数表示的二项式系数可以表示为:

// C++ program to print the pascal triangle // Being a special function, beta is only guaranteed // to be in cmath if the user defines //  __STDCPP_WANT_MATH_SPEC_FUNCS__ before including // any standard library headers. #define __STDCPP_WANT_MATH_SPEC_FUNCS__ 1 #include <bits/stdc++.h> #include <cmath> using namespace std;   // Function to return the value of binomial Coefficient double binomialCoefficient(int n, int k) {     // Calculate the value of nCr using above formula.     double ans = 1 / ((n + 1) * beta(n - k + 1, k + 1));     return ans; } // Driver Code int main() {     // Print the binomial Coefficient nCr where n=5 and r=2     cout << binomialCoefficient(5, 2) << "\n";       return 0; }

输出:

10