On 5/16/06, Barton Willis <willisb at unk.edu> wrote:
>
> (%i38) t : taylor(coth(x) - 1/x,x,0,9);
> (%o38) x/3-x^3/45+(2*x^5)/945-x^7/4725+(2*x^9)/93555+...
> (%i39) revert(%,x);
> (%o39) (126117*x^9+118503*x^7+114345*x^5+121275*x^3+202125*x)/67375
>
> Suggestion: Check revert on some simple cases. Revert might
> be well-tested, but I don't know that it is.
Well, there's an easy way to check the result:
result: %o39$
test: coth(result)+1/result$
taylor(test,x,0,10) => x - 42039*x^9/67375 + ...
Note that error term is x^9, and our original expansion is to x^8, so answer
is correct.
-s