Edit: Changed from Pentation Fixed Points to Tetration Fixed Points. Thanks to JmsNxn for pointing this out
The identity \[z \uparrow \uparrow \infty=\frac{\mathrm{W}(-\ln{z})}{-\ln{z}}\] with some constraints gives a tetration fixed point. To extend this scheme to pentation I believe I need slog, which is fine, but I would also need a generalization of the Lambert W function. Haven't folks on this forum explored hyper or super Lambert W functions.
The identity \[z \uparrow \uparrow \infty=\frac{\mathrm{W}(-\ln{z})}{-\ln{z}}\] with some constraints gives a tetration fixed point. To extend this scheme to pentation I believe I need slog, which is fine, but I would also need a generalization of the Lambert W function. Haven't folks on this forum explored hyper or super Lambert W functions.
Daniel