Andrew Robbins' Tetration Extension

[Gottfried]

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