I also noticed something in that paper where you describe the \( g \)-coefficients for the regular iteration. You have the iterating formula
\( g_n = \frac{1}{{f_1}^n - f_1} \left(f_n {g_1}^n - {g_1}{f_n} + \sum_{m=2}^{n-1} f_m {g^m}_n - g_m {f^m}_n\right) \).
where \( g = reg \)
But at n = 2, we have a sum from "2 to 1". How do you do that? Is it equal to the sum from 2 to 2, minus the value of the summand evaluated at 2 (like how the sum from 2 to 3 is that from 2 to 4 minus the value of the summand at 4)? Wouldn't that just be 0? If I assume so, then I get
\( g_2 = \frac{\log(a)^2 \left(\log(a)^t\right)^2 - \log(a)^t \log(a)^2}{\log(a)^2 - \log(a)} \)
which disagrees with what you gave in your earlier post here.
bo198214: closed one tex tag to make the post readible
\( g_n = \frac{1}{{f_1}^n - f_1} \left(f_n {g_1}^n - {g_1}{f_n} + \sum_{m=2}^{n-1} f_m {g^m}_n - g_m {f^m}_n\right) \).
where \( g = reg \)
But at n = 2, we have a sum from "2 to 1". How do you do that? Is it equal to the sum from 2 to 2, minus the value of the summand evaluated at 2 (like how the sum from 2 to 3 is that from 2 to 4 minus the value of the summand at 4)? Wouldn't that just be 0? If I assume so, then I get
\( g_2 = \frac{\log(a)^2 \left(\log(a)^t\right)^2 - \log(a)^t \log(a)^2}{\log(a)^2 - \log(a)} \)
which disagrees with what you gave in your earlier post here.
bo198214: closed one tex tag to make the post readible
