std::beta, std::betaf, std::betal
From cppreference.com
< cpp | experimental | special functions
double beta( double x, double y ); float betaf( float x, float y ); |
(1) | |
Promoted beta( Arithmetic x, Arithmetic y ); |
(2) | |
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.
Contents |
[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 ∫10tx-1
(1 - t)(y-1)
dt, or, equivalently,
Γ(x)Γ(y) |
Γ(x + y) |
[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(x - 1)!(y - 1)! |
(x + y - 1)! |
⎜
⎝n
k⎞
⎟
⎠=
1 |
(n + 1)Β(n - k + 1, k + 1) |
[edit] Example
(works as shown with gcc 6.0)
Run this code
#define __STDCPP_WANT_MATH_SPEC_FUNCS__ 1 #include <cmath> #include <iomanip> #include <iostream> #include <string> 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'; } }
Output:
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
[edit] See also
(C++11)(C++11)(C++11) |
gamma function (function) |
[edit] External links
Weisstein, Eric W. "Beta Function." From MathWorld--A Wolfram Web Resource.