I recently found out the rule regarding the Taylor expansion of a translated function:(adsbygoogle = window.adsbygoogle || []).push({});

##f(x+h)=f(x)+f′(x)⋅h+\frac 1 2 h^ 2 \cdot f′′(x)+⋯+\frac 1 {n!}h^n \cdot f^n(x)+...##

But why exactly is this the case? The normal Taylor expansion tells us that

##f(x)=f(a)+f'(a)(x-a)+\frac 1 {2!}f''(a)(x-a)^2+...+\frac 1 {n!} f^n(x)(x-a)^n+...##

So how do you come from the original expansion to the second one? Simply substituting x with x+h doesn't do it, not to mention that the f's and the coefficients seem to have changed roles, with the f's now being functions instead of constants and the coefficients now being constants instead of functions.

An explanation would be appreciated.

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# I Taylor expansion of f(x+a)

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