std::beta, std::betaf, std::betal

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

Promoted    beta( Arithmetic x, Arithmetic y );

Parameters

Return value

Error handling

Errors may be reported as specified in math_errhandling.

• If any argument is NaN, NaN is returned and domain error is not reported
• The function is only required to be defined where both x and y are greater than zero, and is allowed to report a domain error otherwise.

Notes

Implementations that do not support C++17, but support ISO 29124:2010, provide this function if __STDCPP_MATH_SPEC_FUNCS__ is defined by the implementation to a value at least 201003L and if the user defines __STDCPP_WANT_MATH_SPEC_FUNCS__ before including any standard library headers.

Implementations that do not support ISO 29124:2010 but support TR 19768:2007 (TR1), provide this function in the header tr1/cmath and namespace std::tr1.

An implementation of this function is also available in boost.math.

beta(x, y) equals beta(y, x) When x and y are positive integers, beta(x,y) equals \(\frac{(x-1)!(y-1)!}{(x+y-1)!}\).

Binomial coefficients can be expressed in terms of the beta function: \(\binom{n}{k} = \frac{1}{(n+1)B(n-k+1,k+1)}\).

Example

#include <cmath>
#include <string>
#include <iostream>
#include <iomanip>
double binom(int n, int k) { return 1/((n+1)*std::beta(n-k+1,k+1)); }
int main()
{
    std::cout << "Pascal's triangle:\n";
    for(int n = 1; n < 10; ++n) {
        std::cout << std::string(20-n*2, ' ');
        for(int k = 1; k < n; ++k)
            std::cout << std::setw(3) << binom(n,k) << ' ';
        std::cout << '\n';
    }
}

Pascal's triangle:
 
                  2 
                3   3 
              4   6   4 
            5  10  10   5 
          6  15  20  15   6 
        7  21  35  35  21   7 
      8  28  56  70  56  28   8 
    9  36  84 126 126  84  36   9

See also

External links

Weisstein, Eric W. "Beta Function." From MathWorld--A Wolfram Web Resource.