09/06/2007, 03:26 AM
@Gottfried
I read your paper, and your first theorem is interesting! Although I couldn't quite follow the "proof", it seems plausible, and I might recommend using an umbral-calculus style of proof. From what I understand umbral calculus is making transitions that are not rigorously true, but strictly syntactic substitutions. For example:
which seems similar to a substitution you make in your paper. I think this would make the proof much clearer, and easier to follow, although I think it has gone out of style, and may be viewed as less rigorous than other methods of proof. I don't know if it helps or not, I just thought I'd comment on it.
Andrew Robbins
I read your paper, and your first theorem is interesting! Although I couldn't quite follow the "proof", it seems plausible, and I might recommend using an umbral-calculus style of proof. From what I understand umbral calculus is making transitions that are not rigorously true, but strictly syntactic substitutions. For example:
\(
\begin{array}{rl}
e^x & = \sum_{k=0}^{\infty} \frac{1}{k!} x^k \\
f(e, x) & = \sum_{k=0}^{\infty} \frac{1}{k!} f(x, k)
\end{align}
\)
\begin{array}{rl}
e^x & = \sum_{k=0}^{\infty} \frac{1}{k!} x^k \\
f(e, x) & = \sum_{k=0}^{\infty} \frac{1}{k!} f(x, k)
\end{align}
\)
which seems similar to a substitution you make in your paper. I think this would make the proof much clearer, and easier to follow, although I think it has gone out of style, and may be viewed as less rigorous than other methods of proof. I don't know if it helps or not, I just thought I'd comment on it.
Andrew Robbins
