How to expand a logarithm with multiple variables in sympy?

Question

I am trying to do the following expansion of the log but other vars disappear for some reason.

Is there something extra about the a, b vars that needs to be included?

Answer 1

You probably want to use the series method rather than Taylor term:

In [15]: from sympy.abc import a, b, c                                                                                                         

In [16]: e = log(1 + a * (b - c**2) / (1 - 1/c))                                                                                               

In [17]: e                                                                                                                                     
Out[17]: 
   ⎛  ⎛     2⎞    ⎞
   ⎜a⋅⎝b - c ⎠    ⎟
log⎜────────── + 1⎟
   ⎜      1       ⎟
   ⎜  1 - ─       ⎟
   ⎝      c       ⎠

In [18]: e.series(c)                                                                                                                           
Out[18]: 
   ⎛   2  2      ⎞      ⎛   3  3                  ⎞      ⎛   4  4              2  2                 ⎞      ⎛   5  5                          
 2 ⎜  a ⋅b       ⎟    3 ⎜  a ⋅b     2  2          ⎟    4 ⎜  a ⋅b     3  3   3⋅a ⋅b     2            ⎟    5 ⎜  a ⋅b     4  4      3  3    3  2
c ⋅⎜- ───── - a⋅b⎟ + c ⋅⎜- ───── - a ⋅b  - a⋅b + a⎟ + c ⋅⎜- ───── - a ⋅b  - ─────── + a ⋅b - a⋅b + a⎟ + c ⋅⎜- ───── - a ⋅b  - 2⋅a ⋅b  + a ⋅b 
   ⎝    2        ⎠      ⎝    3                    ⎠      ⎝    4                2                    ⎠      ⎝    5                            

                             ⎞                
      2  2      2            ⎟            ⎛ 6⎞
 - 2⋅a ⋅b  + 2⋅a ⋅b - a⋅b + a⎟ - a⋅b⋅c + O⎝c ⎠
                             ⎠