Maximally flat magnitude beyond the origin

An all-pole function
T(s)
is presented which has a squared-magnitude low-pass characteristic that is maximally flat at
\omega = b
where
O \leq b < 1
. Expressions for the poles of
T(s)
are given in closed form, and it is shown that they are located on ovals of Cassini.
|T(j |omega)|^{2}
is compared with the Butterworth and Chebyshev functions.