Taylor Expansion Question about this Series

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.
  • #1
LagrangeEuler
717
20
Can you please explain this series
[tex]f(x+\alpha)=\sum^{\infty}_{n=0}\frac{\alpha^n}{n!}\frac{d^nf}{dx^n}[/tex]
I am confused. Around which point is this Taylor series?
 
Physics news on Phys.org
  • #2
LagrangeEuler said:
Can you please explain this series
[tex]f(x+\alpha)=\sum^{\infty}_{n=0}\frac{\alpha^n}{n!}\frac{d^nf}{dx^n}[/tex]
I am confused. Around which point is this Taylor series?

THis is an expansion about [itex]x[/itex]. You can tell that because the series is a power series in [itex]\alpha[/itex].
 
  • #3
It would help if the derivatives were explicitly evaluated at ##x##. Then it would be clearer.
 

Similar threads

  • Calculus
Replies
3
Views
2K
Replies
2
Views
1K
Replies
3
Views
1K
Replies
3
Views
832
Replies
3
Views
1K
Replies
1
Views
1K
Replies
9
Views
1K
Replies
17
Views
3K
Back
Top