MHB How is Rodrigue's Formula Derived?

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SUMMARY

Rodrigues' formula is derived using Legendre polynomials, specifically through the application of differentiation. The formula is expressed as n(x) = (x² - 1)ⁿ, which satisfies the first-order differential equation (1 - x²)f'n + 2nxfn = 0. The discussion emphasizes the importance of understanding the differentiation process involved in this derivation. For further clarification, participants are encouraged to ask additional questions regarding the steps involved.

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Mathematicians, physics students, and anyone interested in advanced calculus and differential equations will benefit from this discussion on the derivation of Rodrigues' formula.

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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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