# ply_legendre_1D Function

## public pure function ply_legendre_1D(points, degree) result(one_dim_eval)

Evaluate all 1D Legendre polynomials at a given set of points up to the given degree.

init the first two Legendre polynomials. ... the first Legendre polynomial is 1

... the second Legendre polynomial is x Recursive polynomial evaluation: \f$n L_{n}(x)= (2n - 1) x L_{n-1}(x) - (n-1)L_{n-2}(x) \f$

### Arguments

TypeIntentOptionalAttributesName
real(kind=rk), intent(in) :: points(:)

1D points to evaluate.

integer, intent(in) :: degree

Degree up to which to evaluate the polynomials

### Return Value real(kind=rk)(degree+1,size(points))

Resulting vector of all mode values at all points

## Variables

TypeVisibilityAttributesNameInitial
integer, private :: iDegree
real(kind=rk), private :: n_q