The legendre , legendref and legendrel are built functions in C++ STL that are used to compute the value of unassociated polynomials of degree n and argument x. Value of order-n unassociated Legendre Polynomial of x is given by :
The first few Legendre polynomials are
double legendre( unsigned int n, double x ) or double legendre( unsigned int n, float x ) or double legendre( unsigned int n, long double x ) or float legendref( unsigned int n, float x ) or long double legendrel( unsigned int n, long double x )
Parameters: The function accepts two mandatory parameters which are described below:
- n: it specifies the degree of the polynomial.
- x: it specifies the argument which denotes a value of a floating-point or integral type
Return Value: The function returns the value of order-n unassociated Legendre Polynomial for argument x. The return type depends on the parameters passed.
Note: The function runs in and above C++ 17(7.1).
Below program illustrates the above mentioned functions:
Errors and Exceptions: The function throws an error on three cases which is described below:
- 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
Below programs illustrate the above errors:
terminate called after throwing an instance of 'std::domain_error' what(): Argument out of range in __poly_legendre_p. legendre(129, 2)=
legendre(129, NaN)= nan
terminate called after throwing an instance of 'std::domain_error' what(): Argument out of range in __poly_legendre_p.