MHB How is Rodrigue's Formula Derived?

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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
 
Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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