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Andrew Robbins' Tetration Extension
#18
Gottfried Wrote:and for
Code:
´  Tb°h(x) = y

the height-function hghT() gives
Code:
´
h = hghT_b(y) = slog_b(y)
           =  log( (g(y')/g(1')) / log(u)
           =  log( (g(y/t-1)/g(1/t-1)) / log(log(t))
Actually this means, the hgh-functions compute the height-differences;
call lgg(x)= log(g(x))/log(u)
then more generally
hghT_b(x1,x0) = lgg(x1') - lgg(x0')
hghU_t(x1,x0) = lgg(x1) - lgg(x0)
and
hghT_b(x) = lgg(x') - lgg(1')
and
hghU_t(x) = lgg(x) - lgg(1)
may be taken as short notations for a default case. (Remember, that the function g and lg are dependent on the base-parameters b and/or t)

Gottfried
Gottfried Helms, Kassel
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Messages In This Thread
Andrew Robbins' Tetration Extension - by bo198214 - 08/07/2007, 04:38 PM
RE: Andrew Robbins' Tetration Extension - by Gottfried - 03/17/2008, 06:09 PM

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