I want to prove this, but I have some questions. If we define $f_n$ like this. $$ f_n = (-1)^n \frac{d^n}{dx^n}(\frac{e^{-x}}{x}) \quad n =0,1,2,... \quad f_0 = \frac{e^{-x}}{x} $$ Prove this. $$ (cond f_n)(f_0) =\frac{1}{|e_n(x)|} , \quad e_n(x) =1 + x + x^2/2! + ... + x^n/n! $$ I know that I should compute $f_n$ with Leibniz formula and it will be $$ f_n = n!\sum_{k = 0}^{n}\frac{e^{-x}}{(n-k)!x^{k+1}} $$ I don't know whether I can use this formula $(cond f)(x) = |\frac{xf'(x)}{f(x)}|$ or I should use the definition of condition number. Can any one help me .I have problem because it wants $(cond f_n)(f_0)$
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