beta(), betaf() and betal() functions in C++ STL
The beta(), betaf() and betal() are built-in functions in C++ STL that are used to compute the beta functionof two positive real values. The function takes two variables x and y as input and returns the beta function of x and y. Beta function (Also known as Euler integral of first kind) of x and y can be defined as:
Syntax
double beta(double x, double y) or long double betal(long double x, long double y) or float betaf(float x, float y)
Parameters: The function accepts two mandatory parameters x and y which specifies the values of a floating-point or integral type. The parameters can be of double, double or float, float or long double, long double data-type.
Return Value: The function returns the value of beta function of x and y. The return type depends on the parameters passed. It is same as that of the parameter.
Note: The function runs in and above C++ 17(7.1).
Below program illustrates the beta(), betaf() and betal() functions:
CPP
// 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; } |
Output:
0.00357143 0.00034965 1.65804e-005
Application of Beta function: It is used to compute Binomial Coefficients.The binomial coefficient in terms of beta function can be expressed as:
The above relation can be used to compute the binomial coefficient. An illustration has been shown below:
CPP
// 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; } |
Output:
10