Is there a built-in function that will find a general expression for the coefficient of the series expansion of a function?
Series
will only give the explicit terms up to some order
In[14]:= Series[Exp[x],{x,0,10}]
Out[14]= 1+x+x^2/2+x^3/6+x^4/24+x^5/120+x^6/720+x^7/5040+x^8/40320+x^9/362880+x^10/3628800+O[x]^11
And GeneratingFunction
works the other way:
In[15]:= GeneratingFunction[1/n!,n,x]
Out[15]= E^x
I'm looking for something like the inverse of GeneratingFunction
: start with Exp[x]
and get 1/n!
. Does it exist?
FindSequenceFunction[]
isn't very clever ... at least in V8. Has it been improved in v9? $\endgroup$ – Dr. belisarius Mar 20 '13 at 2:47FindSequenceFunction
has not been modified since its introduction into V7. $\endgroup$ – m_goldberg Mar 20 '13 at 8:14