Taylor Expansion
Introduction
Taylor expansion around x=0 or Maclaurin expansion.
|x|<x
c
(3.10)
* x
c
:The convergence radius
f(x)
x
c
sin
x
c
=infinity
cos
x
c
=infinity
exp
x
c
=infinity
log
x
c
=1
sinh
x
c
=infinity
cosh
x
c
=infinity
series:
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
function:
sin(x)
cos(x)
exp(x)
log(1+x)
sinh(x)
cosh(x)
return
|x|<xc |x|<xc