Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
ramanujan and tetration
#11
galathaea Wrote:
Code:
by the time he gets to chapter 4
  he is ready to return to iterated exponentiation
and after defining

F (x) = x
0

F   (x) = exp{F (x)} - 1
r+1           r

he decomposes the iteration in two different ways

         oo                 oo
        ---                ---
        \             j    \           j
F (x) = /    phi (r) x   = /    f (x) r
r      ---     j          ---   j
        j=0                j=0

I was really curious how Ramanujan's continuous iteration of would look like. But now I am a bit disappointed. What he considers is not iterated but iterated !
Not that this would be entirely trivial, however this is a case where the function to iterate has a fixed point at 0 and there is only one way to obtain (continuous/fractional/real/complex/analytic) iterates of the formal powerseries and that is regular iteration.

So, though its amazing that he considered the topic of regular iteration at such an early time, he does not contribute towards analytic tetration, where the difficulty is exactly this .
Reply


Messages In This Thread
ramanujan and tetration - by galathaea - 05/28/2008, 08:10 AM
RE: ramanujan and tetration - by Ivars - 05/28/2008, 10:47 AM
RE: ramanujan and tetration - by galathaea - 05/28/2008, 03:19 PM
RE: ramanujan and tetration - by Gottfried - 05/28/2008, 04:12 PM
RE: ramanujan and tetration - by Ivars - 05/28/2008, 05:57 PM
RE: ramanujan and tetration - by galathaea - 05/30/2008, 04:21 AM
RE: ramanujan and tetration - by bo198214 - 05/30/2008, 06:18 AM
RE: ramanujan and tetration - by Ivars - 05/30/2008, 12:38 PM
RE: ramanujan and tetration - by Ivars - 05/29/2008, 06:39 AM
RE: ramanujan and tetration - by Ivars - 05/29/2008, 05:04 PM
RE: ramanujan and tetration - by Ivars - 05/30/2008, 07:23 AM
Thats not tetration! - by bo198214 - 05/30/2008, 07:44 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Iteration by Ramanujan Gottfried 8 8,081 05/28/2008, 06:52 AM
Last Post: bo198214



Users browsing this thread: 1 Guest(s)