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

Technical specifications
Filesystem library (filesystem TS)
Library fundamentals (library fundamentals TS)
Library fundamentals 2 (library fundamentals TS v2)
Library fundamentals 3 (library fundamentals TS v3)
Extensions for parallelism (parallelism TS)
Extensions for parallelism 2 (parallelism TS v2)
Extensions for concurrency (concurrency TS)
Concepts (concepts TS)
Ranges (ranges TS)
Mathematical special functions (special functions TR)
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 );
1) Computes the beta function of x and y.
2) A set of overloads or a function template for all combinations of arguments of arithmetic type not covered by (1). If any argument has integral type, it is cast to double. If any argument is long double, then the return type Promoted is also long double, otherwise the return type is always double.

As all special functions, beta is only guaranteed to be available in <cmath> 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.


[edit] Parameters

x, y - values of a floating-point or integral type

[edit] Return value

If no errors occur, value of the beta function of x and y, that is 1
, or, equivalently,
is returned.

[edit] 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.

[edit] Notes

Implementations that do not support TR 29124 but support TR 19768, 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

Binomial coefficients can be expressed in terms of the beta function:



[edit] Example

(works as shown with gcc 6.0)

#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:
                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

[edit] See also

gamma function
(function) [edit]

[edit] External links

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