1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Evaluating the Svein-Graham Sum

  1. Apr 28, 2015 #1
    Good evening dearest physicians and mathematicians,

    I recently came across the so-called "Svein-Graham sum", and i wondered: is it possible to find a simple formula for evaluating it?
    [itex]\sum_{i=0}^k x\uparrow\uparrow i = \left .1+x+x^x+x^{x^x}+ ... +x^{x^{x^{x^{.^{.^{.^x}}}}}}\right \}k[/itex]
     
  2. jcsd
  3. Apr 29, 2015 #2
    Hi, I use Mathematica to define a function sg[x,k] to calculate the Svein-Graham sum and plot some figures for ##x \in [1,2]## with ##k## varies from 1 to 5.
    Code (Text):
    sg[x_, k_] := Module[{f},
      f[y_] := #^y &;
      (FoldList[f[x], x, Range[k - 1]] // Total) + 1]
    Plot[sg[x, #], {x, 1, 2}] & /@ Range[1, 5]
     
    Last edited: Apr 29, 2015
  4. Apr 29, 2015 #3
    I was looking for a more analytic expression like [itex]\sum_{i=1}^n i = \frac{n(n+1)}{2}[/itex]. Maybe it's possible to find yet another connection to the Bernoulli numbers? But thank you nevertheless!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Evaluating the Svein-Graham Sum
  1. Sum evaluation help (Replies: 2)

Loading...