Rodrigues' formula
From Wikipedia, the free encyclopedia
Rodrigues' formula has two possible meanings:
- In geometry, short for Rodrigues' rotation formula.
- A formula for producing a series of expressions by repeated differentiation of some other functions. A typical application is in producing a series of orthogonal polynomials. In particular,
![P_n(x) = \frac{1}{a_n W(x)} \ \frac{d^n}{dx^n}\left(W(x)[Q(x)]^n\right)](../../../../math/e/7/a/e7af924eb2e4fc66235d403f4cf8a073.png)
for some functions W, Q, and constants an.
Both of these were discovered by Olinde Rodrigues.
