Re: Tetration again!

On Dec 21, 1:47 am, Gottfried Helms <he...@xxxxxxxxxxxxx> wrote:
Am 20.12.2007 20:14 schrieb galathaea:



one was issued by the tata institute
  just as a photocopy
the other is a nicely edited one by bruce berndt

the berndt editing has known proofs
  and other very useful exposition
separated into 5 books

chapter 4 of ramanujan's notebooks
is found in book 1 of berndt
  which he titles:
"iterates of the exponential function
 and an ingenious formal technique"

entries 1 thru 7 (and their corollaries)
  give his basic results
  including basic recursions
    series identities
    an integral formula
    and (as always for ramanujan) asymptotics

Ah - thank you very much!


Hmm. Does this mean the true solution of tetration
was already discovered, a real long time ago?

What would be really interesting is if this method applies
more generally to iterating functions continuously *and*
reproduces the first 3 hyper operators when applied
to their iterations, ex. for multiplication we
iterate f(x) = b + x, for exponentiation we iterate
f(x) = bx, and the results agree exactly with the
widely-accepted definitions.
.

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