Change of base formula for Tetration

[jaydfox]

I'm curious to see this function graphed, once we've put together the tools to solve the various bases. We're almost there. This graph would appear to grow hyperexponentially to the right, but asymptotically approaches eta to the left. In some ways, I bet this graph looks more interesting than the tetration graph, because the curvature should always be positive.

Random guess, before I go to bed. This function seems very similar to the cheta function. It's asymptotic to the left, hyperexponential to the right. The asymptote itself is different, so there may be some scaling involved, and possibly some other small changes. Something for me to ponder over the next few days...