Home > Preview
The flashcards below were created by user
on FreezingBlue Flashcards.
- If f has a power series representation (expansion) at a, that is, if: f(x) = cn(x - a)n | x - a| < R THEN its coefficients are given by the formula: cn = f(n)(a) / n!
Formula 6 - Taylor series of the function f at a
- f(x) = ( f(n)(a) / n! ) (x - a)n
- = f(a) + ( f ' (a) / 1! ) ( x - a) + ( f '' (a) / 2! ) ( x - a)2 + ( f ''' (a) / 3! ) ( x - a)3 + ...
Formula 7 - Taylor series of the function f at 0 (Maclaurin series)
- f(x) = ( f(n)(0) / n! ) xn
- = f(0) + ( f ' (0) / 1! ) x + ( f '' (0) / 2! ) ( x)2 + ( f ''' (0) / 3! ) ( x)3 + ...
if f(x) = Tn(x) + Rn(x), where Tn is the nth-degree Taylor polynomial of f at a and lim(n->infinity) Rn(x) = 0 for |x-a| < R, the f is equal to the sum of its Taylor series on the interval |x-a| < R
What would you like to do?
Home > Flashcards > Print Preview