Let u(x)=1+ x 2. + 5! 3! v(x)=1+ + 2! 2.2 d dx + + 23...

 

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Let u(x)=1+ x 2. + 5! 3! v(x)=1+ + 2! 2.2 d dx + + 23 7! 6! +... = + = n=0 n=0 (2n+1)! xn (2n)! (1) Show that (u(x)x ) _ v(x) xu(x) 2v (x) x (Note that u(x)= (u(x)),v(x) = (v(x))) and for x>0. Let u(x)=1+ x 2. + 5! 3! v(x)=1+ + 2! 2.2 d dx + + 23 7! 6! +... = + = n=0 n=0 (2n+1)! xn (2n)! (1) Show that (u(x)x ) _ v(x) xu(x) 2v (x) x (Note that u(x)= (u(x)),v(x) = (v(x))) and for x>0.