Hi,
just a couple of days ago I felt obliged to answer one question in MSE, where some member showed his conditions & equations coming from analysis of the tetration-mathematics.
After some detective/investigation I understood that he attempted to set up an Abel-equation.
To give him an impression of a way to solve it for the coefficients of the Abel-function (and its inverse) I "reengineered" Andy Robbins' method and showed some values from his slog() function.
However, I went one step further and calculated the inverse powerseries for his slog() (where the constant term was removed), and surprisingly found a nice function for the tetration: \[\phi(x) = \,^x e\]
with a nice computational behave.
It is a long text, but if this would be interesting for our forum, I could transfer this answer to our forum, may be at one of Andydude's JayDFox's threads where they explained their method (hints for a good place are then welcome).
Gottfried
just a couple of days ago I felt obliged to answer one question in MSE, where some member showed his conditions & equations coming from analysis of the tetration-mathematics.
After some detective/investigation I understood that he attempted to set up an Abel-equation.
To give him an impression of a way to solve it for the coefficients of the Abel-function (and its inverse) I "reengineered" Andy Robbins' method and showed some values from his slog() function.
However, I went one step further and calculated the inverse powerseries for his slog() (where the constant term was removed), and surprisingly found a nice function for the tetration: \[\phi(x) = \,^x e\]
with a nice computational behave.
It is a long text, but if this would be interesting for our forum, I could transfer this answer to our forum, may be at one of Andydude's JayDFox's threads where they explained their method (hints for a good place are then welcome).
Gottfried
Gottfried Helms, Kassel
