07/07/2011, 03:56 AM
Oh no, this isn't that at all 
This is just a simple formula to change the base of a power tower for natural integers.
however, this does provide an interesting continuum like sum for:
\( f(z) = x \cdot \ln(b) + \ln^{\circ 2}(b)\,\,\bigtriangleup_{-1}^e\,\,\ln^{\circ 3}(b)\,\,\bigtriangleup_{-2}^e\,\,\ln^{\circ 4}(b)...\,\,\bigtriangleup_{2-z}^e\,\,\ln^{\circ z}(b) \)
where f(z) is given by:
\( f(z) = \exp_e^{\circ -z}(\exp_b^{\circ z}(x)) \)
mike noted that as z goes to infinity, f(z) converges if x=1 and b=3.
I've seen these alternating operators before. They seem very intimidating, but I feel like there's something powerful about 'em.
This is just a simple formula to change the base of a power tower for natural integers.
however, this does provide an interesting continuum like sum for:
\( f(z) = x \cdot \ln(b) + \ln^{\circ 2}(b)\,\,\bigtriangleup_{-1}^e\,\,\ln^{\circ 3}(b)\,\,\bigtriangleup_{-2}^e\,\,\ln^{\circ 4}(b)...\,\,\bigtriangleup_{2-z}^e\,\,\ln^{\circ z}(b) \)
where f(z) is given by:
\( f(z) = \exp_e^{\circ -z}(\exp_b^{\circ z}(x)) \)
mike noted that as z goes to infinity, f(z) converges if x=1 and b=3.
I've seen these alternating operators before. They seem very intimidating, but I feel like there's something powerful about 'em.
