09/21/2007, 02:01 PM

Dear Gottfried, Andrew and Henryk,

I was impressed by the last plot posted by you (Gottfried) and I am pleased to tell you that I agree completely with your conclusions. Please find attached some notes concerning that matter. Actually, the same result can be reached from another end, by using the two real branches of the product-logarithm (Lambert) function. Therefore, I presume that the plot is correct.

Nevertheless, by using the same method, it seems that for b -> oo the complex infinite towers don't vanish, as it could be felt from a first look at your graph. Is it correct? Can that be proved?

Best wishes.

Gianfranco

I was impressed by the last plot posted by you (Gottfried) and I am pleased to tell you that I agree completely with your conclusions. Please find attached some notes concerning that matter. Actually, the same result can be reached from another end, by using the two real branches of the product-logarithm (Lambert) function. Therefore, I presume that the plot is correct.

Nevertheless, by using the same method, it seems that for b -> oo the complex infinite towers don't vanish, as it could be felt from a first look at your graph. Is it correct? Can that be proved?

Best wishes.

Gianfranco