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• LagrangeEuler
In summary, Taylor expansion is a mathematical concept used to approximate a function at a specific point by representing it as an infinite sum of terms. It is useful in many areas of mathematics, physics, and engineering and is calculated by finding the coefficients of a polynomial function through derivatives. It is a generalization of Maclaurin Expansion and has applications in various fields such as calculating derivatives and integrals, finding critical points, and data analysis.
LagrangeEuler
Can you please explain this series
$$f(x+\alpha)=\sum^{\infty}_{n=0}\frac{\alpha^n}{n!}\frac{d^nf}{dx^n}$$
I am confused. Around which point is this Taylor series?

LagrangeEuler said:
Can you please explain this series
$$f(x+\alpha)=\sum^{\infty}_{n=0}\frac{\alpha^n}{n!}\frac{d^nf}{dx^n}$$
I am confused. Around which point is this Taylor series?

THis is an expansion about $x$. You can tell that because the series is a power series in $\alpha$.

It would help if the derivatives were explicitly evaluated at ##x##. Then it would be clearer.

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