The Lambert W-Function

Follow on twitter: @thatsmaths In a recent post ( The Power Tower ) we described a function defined by iterated exponentiation: $latex \displaystyle y(x) = {x^{x^{x^{.^{.^{.}}}}}} &fg=000000$ It would seem that when $latex {x>1}&fg=000000$ this must blow up. Surprisingly, it has finite values for a range of x>1. Below, we show that the power tower…