MHB How is Rodrigue's Formula Derived?

[danny12345]

View attachment 4812
how do we derive rodrigue's formula

 

[Sudharaka]

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. :)

 

[danny12345]

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