Proving using rodrigue's formula (a very challenging question)

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The discussion centers on proving the equation (n+1)Pn+1(x)-(2n+1)xPn(x)+nPn-1(x)=0 using Rodriguez's formula. The original poster expresses difficulty with differentiation but has made progress by finding a formula that enables them to differentiate multiple times. They are currently focused on determining Pn+1 and Pn-1 using Rodriguez's formula and plan to substitute these back into the equation. There is a back-and-forth about the challenges of differentiation, with encouragement to share specific attempts. The thread highlights the complexity of the problem and the collaborative effort to find a solution.
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This is a very challenging question I would like your help guys to solve this question.
Prove (n+1)Pn+1(x)-(2n+1)xPn(x)+nPn-1(x)=0 using Rodriguez's formula
 
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What have you tried so far?
 
The problem is in differentiating ..I really find it very difficult to differentiate..
 
You still haven't said what you tried. Or are you saying that, because you are "find it very difficult to differentiate", you simply haven't tried at all?
 
I am making a progress .. I found a formula that allowed me to differentiate (n+1) times, so now am working on finding Pn+1 and Pn-1 by the Rodriguez formula , and then substituting them back in the equation..
 

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