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..
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