Table 1 Examples of generalized linear systems

Generating function ϕ(x)

\(\log (x)\)

\(-\log (1-x)\)

\(-\log \frac {1-x}{\eta x}\)

\(-\text {sign}(x)\log (1-|x|)\)

Domain

x>0

\(-\infty <x<1\)

0<x<1

−1<x<1

Identity element I

1

0

1/(1+η)

0