std:: legendre, std:: legendref, std:: legendrel

As all special functions, legendre 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.

Parameters

Return value

Error handling

Errors may be reported as specified in math_errhandling .

• If the argument is NaN, NaN is returned and domain error is not reported.
• The function is not required to be defined for |x| > 1 .
• If n is greater or equal than 128, the behavior is implementation-defined.

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 .

The first few Legendre polynomials are:

• legendre(0, x) = 1 .
• legendre(1, x) = x .
• legendre(2, x) =

  1

  2

  (3x 2 - 1) .
• legendre(3, x) =

  1

  2

  (5x 3 - 3x) .
• legendre(4, x) =

  1

  8

  (35x 4 - 30x 2 + 3) .

Example

#define __STDCPP_WANT_MATH_SPEC_FUNCS__ 1
#include <cmath>
#include <iostream>
 
double P3(double x)
{
    return 0.5 * (5 * std::pow(x, 3) - 3 * x);
}
 
double P4(double x)
{
    return 0.125 * (35 * std::pow(x, 4) - 30 * x * x + 3);
}
 
int main()
{
    // spot-checks
    std::cout << std::legendre(3, 0.25) << '=' << P3(0.25) << '\n'
              << std::legendre(4, 0.25) << '=' << P4(0.25) << '\n';
}

-0.335938=-0.335938
0.157715=0.157715

See also

External links