10/31/2009, 10:38 AM
This is probably an old result. For the function
\( AS(x) = \sum_{k=0}^{\infty} (-1)^k ({}^{k}x) \)
I found using Carleman matrices that
\( AS(x+1) = 1 + x^2 + \frac{1}{2}x^3 + \frac{4}{3}x^4 + \frac{19}{12}x^5 + \cdots \)
is this related to the series above?
\( AS(x) = \sum_{k=0}^{\infty} (-1)^k ({}^{k}x) \)
I found using Carleman matrices that
\( AS(x+1) = 1 + x^2 + \frac{1}{2}x^3 + \frac{4}{3}x^4 + \frac{19}{12}x^5 + \cdots \)
is this related to the series above?