MHB How is Rodrigue's Formula Derived?

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Rodrigues' formula can be derived using Legendre polynomials, which are defined by the equation n(x)=(x^2-1)^n. The derivation involves differentiating this equation, leading to a first-order differential equation: (1-x^2)f'n + 2nxfn = 0. Clarification was requested regarding the differentiation process used in the derivation. Further questions about the derivation are welcomed for additional explanation.
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how do we derive rodrigue's formula
 

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dansingh said:
how do we derive rodrigue's formula

Hi dansingh,

Welcome to MHB! The method of deriving this is given at this link;

Legendre polynomials and Rodrigues' formula

Let us know if you have any further questions with the derivation. :)
 
n(x)=(x2-1)n. (20)

By differentiation we see that it satisfies the following first order differential equation,
(1-x2)f'n+2nxfn=0.
how did you get itb pleasez explain me the differentiation part
 

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