 Closely related to the Legendre polynomials are associated Legendre polynomials, Legendre functions, Legendre functions of the second kind, and associated Legendre functions.In this approach, the polynomials are defined as an orthogonal system with respect to the weight function formula_1 over the interval formula_2.That is, formula_3 is a polynomial of degree formula_4, such that

This determines the polynomials completely up to an overall scale factor, which is fixed by the standardization
formula_6.