let give f(x)= (1/(1+x^2 )) 1)prove that prove that f^((n)) (x)=((p_n (x))/((1+x^2 )^(n+1) )) with p_n is a polynomial 2) prove that p_(n+1) (x)=(1+x^2 )p_n ^′ (x) −2(n+1)p_n (x) 3) calculate p_0 (x) ,p_1 (x) ,p_2 (x) ,p


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Question Number 29831 by abdo imad last updated on 12/Feb/18

$l e t g i v e f (x) = \frac{1}{1 + x^{2}} 1) p r o v e t h a t p r o v e t h a t$ $f^{(n)} (x) = \frac{p_{n} (x)}{{(1 + x^{2})}^{n + 1}} w i t h p_{n} i s a p o l y n o m i a l$ $2) p r o v e t h a t p_{n + 1} (x) = (1 + x^{2}) p_{n}^{^{'}} (x) - 2 (n + 1) p_{n} (x)$ $3) c a l c u l a t e p_{0} (x), p_{1} (x), p_{2} (x), p_{3} (x) .$
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