To prove the non result for the above integral we will make use of the Rodriguez formula and then will integrate by parts Total n-1 successive derivatives over the factor will leave at lease one factor in all the terms generated from the first term of the above expression. Dk1 dxk1 2k 1x2 1x2 1k2 For k n1 we get P n1x 1 2n n. If v is a vector in ℝ3 and k is a unit vector describing an axis of rotation about which v rotates by an angle th according to the right hand rule the Rodrigues formula is.
Derivation of the Euler-Rodrigues formula for three-dimensional rotations from the general formula for four-dimensional rotations.
Instead of solving the recursion relation 1-54 for the coefficients in the Legendre polynomials it is easier to use the following trick. Dk dxk xx2 1k1 1 2k1 k 1. In mathematics Rodrigues formula formerly called the IvoryJacobi formula is a formula for the Legendre polynomials independently introduced by Olinde Rodrigues Sir James Ivory and Carl Gustav Jacobi The name Rodrigues formula was introduced by Heine in 1878 after Hermite pointed out in 1865 that Rodrigues was the first to discover it. Legendre polynomials and Rodrigues formula.