08/21/2007, 06:08 PM
andydude Wrote:\(
A_n = \sum_{k=n}^{\infty} \left({k \atop n}\right) \sum_{j=0}^k \left{{k \atop j}\right} \frac{j!}{k!} A_j
\)
It sounds a bit like nit picking, but if we solve this equation system in the natural way (as limit of equation systems of increasing size as you explained it with the Cramer's rule), do we then get the slog (as developed by you at 0) developed at the point 1?
My point is: Infinite equation systems have several solutions. For your slog you used the most natural way of solving the equation system for an development at 0. Now you show that one can impose such an equation system at any development point \( x_0 \). The question is whether the resulting developments all belong to the same analytic function (which I heavily guess.)
