Wolfram Function Repository
Instantuse addon functions for the Wolfram Language
Function Repository Resource:
Find a numerical approximation of a series expansion of a function
ResourceFunction["NSeries"][f,{x,x_{0},n}] gives a numerical approximation to the series expansion of f about the point x=x_{0} including the terms (xx_{0})^{n} through (xx_{0})^{n}. 
"Radius"  1  radius of circle on which f is sampled  
WorkingPrecision  MachinePrecision  precision used in internal computations 
This is a power series for the exponential function around x=0:
In[1]:= 

Out[1]= 

Chop is needed to eliminate spurious residuals:
In[2]:= 

Out[2]= 

Using extended precision may also eliminate spurious imaginaries:
In[3]:= 

Out[3]= 

Find expansions in the complex plane:
In[4]:= 

Out[4]= 

Find Laurent expansions about essential singularities:
In[5]:= 

Out[5]= 

Series will not find Laurent expansions about essential singularities:
In[6]:= 

Out[6]= 

Use "Radius" to pick the annulus within which the Laurent series will converge:
In[7]:= 

Out[7]= 

Laurent series for x≥3:
In[8]:= 

Out[8]= 

Changing "Radius" can improve accuracy:
In[9]:= 

Out[9]= 

In[10]:= 

Out[10]= 

A function defined only for numerical input:
In[11]:= 

Find a series expansion of f:
In[12]:= 

Out[12]= 

Check:
In[13]:= 

Out[13]= 

NResidue can also be used to construct a series of a numerical function:
In[14]:= 

In[15]:= 

Out[15]= 

Using NResidue:
In[16]:= 

Out[16]= 

NSeries can have aliasing problems due to InverseFourier:
In[17]:= 

Out[17]= 

The correct expansion is analytic at the origin:
In[18]:= 

Out[18]= 

SeriesData cannot correctly represent a Laurent series. Here is the square of the series of Exp:
In[19]:= 

Out[19]= 

Here is the SeriesData representation of the Laurent series of Exp:
In[20]:= 

Out[20]= 

Find the series expansion of the generating function for unrestricted partitions:
In[21]:= 

In[22]:= 

Out[22]= 

Check:
In[23]:= 

Out[23]= 

Wolfram Language 11.3 (March 2018) or above
This work is licensed under a Creative Commons Attribution 4.0 International License