Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
holomorphic binary operators over naturals; generalized hyper operators
#8
I think the following will work to show convergeance

assume x , y and s to be reals > eta

1) the value of the product = 0 => done

2) the value is not zero => take the log => we get a sum

2b) show that the tail of the sequence goes to 0 faster than constant / n^2 hence we have convergeance. ( because of the famous Basel problem " zeta(2) = Pi^2 / 6 " )

As for the recursion , i dont know if it helps but remember

to go from s+1 to s do :

( we take the inverse with respect to y , notation : ^-1 )

f(x,y,s) = f(x,f^-1(x,y,s)+1,s)

which should be valid for all sufficiently large real non-integer s too.

regards

tommy1729
Reply


Messages In This Thread
RE: holomorphic binary operators over naturals; generalized hyper operators - by tommy1729 - 07/21/2012, 03:42 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Thoughts on hyper-operations of rational but non-integer orders? VSO 2 138 09/09/2019, 10:38 PM
Last Post: tommy1729
  Can we get the holomorphic super-root and super-logarithm function? Ember Edison 10 1,558 06/10/2019, 04:29 AM
Last Post: Ember Edison
  Where is the proof of a generalized integral for integer heights? Chenjesu 2 628 03/03/2019, 08:55 AM
Last Post: Chenjesu
  Hyper-volume by integration Xorter 0 1,219 04/08/2017, 01:52 PM
Last Post: Xorter
  Hyper operators in computability theory JmsNxn 5 3,437 02/15/2017, 10:07 PM
Last Post: MphLee
  Recursive formula generating bounded hyper-operators JmsNxn 0 1,328 01/17/2017, 05:10 AM
Last Post: JmsNxn
  Rational operators (a {t} b); a,b > e solved JmsNxn 30 35,332 09/02/2016, 02:11 AM
Last Post: tommy1729
  The bounded analytic semiHyper-operators JmsNxn 2 3,264 05/27/2016, 04:03 AM
Last Post: JmsNxn
  on constructing hyper operations for bases > eta JmsNxn 1 2,438 04/08/2015, 09:18 PM
Last Post: marraco
  Bounded Analytic Hyper operators JmsNxn 25 17,980 04/01/2015, 06:09 PM
Last Post: MphLee



Users browsing this thread: 1 Guest(s)