There is a way, using Mathematica to make a long division by increasing power order. For example, if I want to divide 1 by x^2 + 1?
Series[1/(x^2+1), {z,0,5}] or something like that?
Thanks, I am looking for the coefficients of the division of 1 by 1+ x^2, using long division or division by increasing power order. To get the coefficients, I am looking for the result of the long division of 1 by 1+x^2. I get: 1/2-(1/4)x^2 + (1/8)x^4 -(1/16)x^6+ ... This is not the inverse series as the command Mathematica has. You can get the same result using Cauchy's Product Formula. If A is the series, then I/A will be the series I am looking for. If 1/A = B, then 1 = AB, and by Cauchy's Product formula I get the values of the coefficients of series B. Hope this clarify.
That appears to be the series for 1/(2+x^2).
1/(2+x^2)
In[5]:= Series[1/(2+x^2),{x,0,8}]//InputForm Out[5]//InputForm= SeriesData[x, 0, {1/2, 0, -1/4, 0, 1/8, 0, -1/16, 0, 1/32}, 0, 9, 1]
Thank you, very much.
