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+--- Thread: 1960s stuff on extending tetration to real height? (/showthread.php?tid=432)
1960s stuff on extending tetration to real height? - mike3 - 03/23/2010
Hi.
I saw this really interesting 1-page preview from 1969(!):
http://www.jstor.org/pss/2004405
where it mentions methods and tables for the evaluation of a function "F(x)" such that "F(0) = 0", "F(1) = 1", "F(2) = e", "\( F(e) = e^e \)" -- look familiar? Yeah, it's the tetrational function, just offset by 1. And they mention about evaluating it at fractional values, and also reference another work which supposedly contains another extension giving different values. I wonder, did they get 1.646354... for \( ^{1/2} e \)?
However it costs $24 to get the full article from this site
If anyone has any access to this (like at an academic library), would they be interesting in checking it out? Based on what it says, I'm not sure if the tables are included here or not since it looks to reference something else containing the tables called "Tables for Continuously Iterating the Exponential and Logarithm".
RE: 1960s stuff on extending tetration to real height? - Ztolk - 03/23/2010
I have access to JSTOR but it appears that just this half page review is there.
It says "Deposited in UMT file," which when googled will come up in a bunch of JSTOR reviews of other typewritten documents. I think it refers to Unpublished Mathematical Tables. I think I have access to that too, let me have a look.
Ok. The most recent Unpublished Mathematical Tables in JSTOR is 1954, and this review is 1969. You'll probably have to do some wizardry to find a hard copy.
RE: 1960s stuff on extending tetration to real height? - andydude - 03/25/2010
Yes, I have heard of this review. In my head I store it as the Fuller-Ward review. But since I have never been able to obtain the "tables" which are being reviewed, I haven't been able to determine whether or not this is linear tetration (offset by 1) or if it is a more continuous/differentiable extension of tetration.
Andrew Robbins
RE: 1960s stuff on extending tetration to real height? - andydude - 03/25/2010
PS. No, that page is the entire review. There are no table attached.
RE: 1960s stuff on extending tetration to real height? - mike3 - 03/25/2010
(03/25/2010, 12:56 AM)andydude Wrote: PS. No, that page is the entire review. There are no table attached.
But it's a review of a work, isn't it? Couldn't you get that work? Or is it too obscure or something?
RE: 1960s stuff on extending tetration to real height? - Ztolk - 03/25/2010
It's in something called Unpublished Mathematical Tables, and I have access to that up to 1954, and each one of those is full of similar reviews, but I'm not sure where they're actually stored.
RE: 1960s stuff on extending tetration to real height? - bo198214 - 03/25/2010
(03/25/2010, 12:56 AM)andydude Wrote: But since I have never been able to obtain the "tables" which are being reviewed, I haven't been able to determine whether or not this is linear tetration (offset by 1) or if it is a more continuous/differentiable extension of tetration.
ya would really interesting to see which method Fuller and also Zavrotsky applied.
(03/25/2010, 02:20 AM)mike3 Wrote: But it's a review of a work, isn't it? Couldn't you get that work? Or is it too obscure or something?
Both works, Fuller's and of Zavrotski's, are neither listed in AMS Reviews nor in Zentralblatt.
Would really difficult to locate them.
For Fuller's (which is reviewed on the page) it is not even clear for me in which Journal and in which year it is published. Is thtis page a review articles in "Mathematics of Computation"? So would one expect Fuller's article there? (Zavrotski's seems also have to do with MOC, but I guess nobody is able to understand the Spanish article.)
RE: 1960s stuff on extending tetration to real height? - mike3 - 03/25/2010
(03/25/2010, 10:03 AM)bo198214 Wrote: Both works, Fuller's and of Zavrotski's, are neither listed in AMS Reviews nor in Zentralblatt.
Would really difficult to locate them.
For Fuller's (which is reviewed on the page) it is not even clear for me in which Journal and in which year it is published. Is thtis page a review articles in "Mathematics of Computation"? So would one expect Fuller's article there? (Zavrotski's seems also have to do with MOC, but I guess nobody is able to understand the Spanish article.)
I don't know since I don't have access to an academic library.