Rodrigues formula [rə′drē·gəs ‚fȯr·myə·lə]
Rodrigues Formula
(mathematics)
The equation giving thenth function in a class of special functions in terms of thenth derivatives of some polynomial.
The formuladn+k dr= 0, expressing the differencednin the unit normals to a surface at two neighboring points on a line of curvature, in terms of the differencedrin the position vectors of the two points and the principal curvaturek.
The formula for a matrix that is used to transform the cartesian coordinates of a vector in three-space under a rotation through a specified angle about an axis with specified direction cosines.
Rodrigues Formula
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.
Want to thank TFD for its existence? Tell a friend about us, add a link to this page, add the site to iGoogle, or visit the webmaster's page for free fun content.
| ?Page tools | ||
|---|---|---|
|