The Rodrigues' formula is either of the following:
- 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)[\alpha(x)]^n\right)](http://wpcontent.answers.com/math/5/4/3/5438dc633f06e9319f27aacb7314c47c.png)
- for some functions w, α, and constants an.
- In particular, for Sturm–Liouville systems
- the polynomial solutions are generated as above.
Both of these were discovered by Olinde Rodrigues.
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