Rodrigues formula[rə′drē·gəs ‚fȯr·myə·lə]
the expression for Legendre polynomials
This formula was derived by the French mathematician B. O. Rodrigues in 1814. In 1859 the German mathematician K. Jacobi extended the formula to the case of Jacobi polynomials. In this case, it has the form
The Rodrigues formula can be incorporated into the theory of Legendre and Jacobi polynomials; in particular, by using the formula it is a simple matter to derive the basic properties of these polynomials. It also follows from the formula that these polynomials are special cases of the hypergeometric function.