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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-c

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Question Number 29831 by abdo imad last updated on 12/Feb/18
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_3 (x) .
letgivef(x)=11+x21)provethatprovethatf(n)(x)=pn(x)(1+x2)n+1withpnisapolynomial2)provethatpn+1(x)=(1+x2)pn′(x)−2(n+1)pn(x)3)calculatep0(x),p1(x),p2(x),p3(x).

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