std::laguerre,std::laguerref,std::laguerrel (3) - Linux Manuals

std::laguerre,std::laguerref,std::laguerrel: std::laguerre,std::laguerref,std::laguerrel

NAME

std::laguerre,std::laguerref,std::laguerrel - std::laguerre,std::laguerref,std::laguerrel

Synopsis

double laguerre( unsigned int n, double x );
float laguerre( unsigned int n, float x );
long double laguerre( unsigned int n, long double x ); (1) (since C++17)
float laguerref( unsigned int n, float x );
long double laguerrel( unsigned int n, long double x );
double laguerre( unsigned int n, IntegralType x ); (2) (since C++17)

1) Computes the non-associated Laguerre_polynomials of the degree n and argument x
2) A set of overloads or a function template accepting an argument of any integral_type. Equivalent to (1) after casting the argument to double.

Parameters

n - the degree of the polymonial, a value of unsigned integer type
x - the argument, a value of a floating-point or integral type

Return value

If no errors occur, value of the nonassociated Laguerre polynomial of x, that is

ex
n!

dn
dxn

(xn
e-x), is returned.

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
* If x is negative, a domain error may occur
* If n is greater or equal than 128, the behavior is implementation-defined

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
The Laguerre polynomials are the polynomial solutions of the equation xy,,
+(1-x)y,
+ny = 0
The first few are:

* laguerre(0, x) = 1
* laguerre(1, x) = -x + 1
* laguerre(2, x) =

  1
  2

  [x2
  -4x+2]
* laguerre(3, x) =

  1
  6

  [-x3
  -9x2
  -18x+6]

Example

// Run this code

  #define __STDCPP_WANT_MATH_SPEC_FUNCS__ 1
  #include <cmath>
  #include <iostream>
  double L1(double x) { return -x + 1; }
  double L2(double x) { return 0.5*(x*x-4*x+2); }
  int main()
  {
      // spot-checks
      std::cout << std::laguerre(1, 0.5) << '=' << L1(0.5) << '\n'
                << std::laguerre(2, 0.5) << '=' << L2(0.5) << '\n';
  }

Output:

  0.5=0.5
  0.125=0.125

External links

Weisstein,_Eric_W._"Laguerre_Polynomial." From MathWorld--A Wolfram Web Resource.