Steve W. writes: << This is the tower-of-exponentials I'm playing with now: (*) fe(x) = 2 sinh( fe( x - tanh( x/2 ) ) ) As x --> +oo, fe(x) --> e^f( x-1 ), as x --> -oo, fe(x) --> -e^-f( x+1 ) (or just -f(-x)), and as x --> 0, fe(x) --> 2 fe( x/2 ). To calculate despite the circular definition, I assume a straight line with some slope when abs(x) < 2^-27, where sinh and tanh are linear enough that the location of the seam is invisible to floating point.
Is it clear that the functional equation I've labeled (*) has a unique solution fe ? --Dan ________________________________________________________________________________________ "Outside of a dog, a book is man's best friend. Inside of a dog, it's too dark to read." --Groucho Marx