( |  |
piqritau(q)(ln(pi))/( |
 |
piqritau(q)(ln(ri))
= |
|
(( |  |
piqritau(q)(ln(pi))/( |
 |
piqritau(q)(ln(ri))) * (ln(ra)/ln(pa)) *
(ln(pa)/ln(ra))
= |
|
(( |  |
piqritau(q)(ln(pi)*ln(ra))/( |
 |
piqritau(q)(ln(ri)*ln(pa))) *
(ln(pa)/ln(ra))
>= |
|
(( |  |
piqritau(q)(ln(pa)*ln(ri))/( |
 |
piqritau(q)(ln(ri)*ln(pa))) *
(ln(pa)/ln(ra))
= |
|
ln(pa)/ln(ra) |
The inequality alpha <= max{ln(pi)/ln(ri)} is handled similarly. |
Combining these bounds we obtain |
alphamin <= alpha <= alphamax |