Taylor Series are Limits of Legendre Expansions - Gvsu - Grand ...

Taylor’s Theorem
If f is analytic in the open disk of radius R > 0 , then we
may write for z in this disk,
f(z) =
∞∑
n=0
a n z n ,
2
where
y
–2 –1 0 1 2
x
–1
–2
1
a n = f(n) (0)
n!
and
1
R = lim
n→∞ |a n| 1 n .
Taylor Series areLimits of Legendre Expansions – p.3/15