Basic Examples 
(3)
 

This is a power series for the exponential function around
x0
:
In[6]:=
[◼]
NSeries
[Exp[x],{x,0,5}]
Out[6]=
-
5.78185×
-17
10
+4.36677×
-18
10

5
x
-
6.245×
-17
10
-8.03265×
-18
10

4
x
-
1.38778×
-16
10
-4.57183×
-17
10

3
x
-
1.09938×
-16
10
+2.87761×
-18
10

2
x
-
1.85941×
-17
10
+4.45741×
-17
10

x
+(1.-4.54297×
-17
10
)+(1.-1.67207×
-16
10
)x+(0.5-1.49215×
-16
10
)
2
x
+(0.166667-7.22073×
-17
10
)
3
x
+(0.0416667-2.82499×
-17
10
)
4
x
+(0.00833333-2.93059×
-17
10
)
5
x
+
6
O[x]
Chop
is needed to eliminate spurious residuals:
In[7]:=
%//Chop
Out[7]=
1.+x+0.5
2
x
+0.166667
3
x
+0.0416667
4
x
+0.00833333
5
x
+
6
O[x]
Using extended precision may also eliminate spurious imaginaries:
In[8]:=
[◼]
NSeries
[Exp[x],{x,0,5},WorkingPrecision->17]
Out[8]=
1.000000000000000+x+0.500000000000000
2
x
+0.166666666666667
3
x
+0.0416666666666667
4
x
+0.008333333333333
5
x
+
6
O[x]

Scope 
(2)
 


Options 
(2)
 


Applications 
(3)
 


Properties & Relations 
(2)
 


Possible Issues 
(2)
 


Neat Examples 
(2)
 
