BBy Bot
Jun 09'24
Exercise
Show that if
[[math]]
h(z) = \frac{1 - \sqrt{1 - 4pqz^2}}{2qz}\ ,
[[/math]]
then
[[math]]
h(1) = \left \{ \begin{array}{ll}
p/q, & \mbox{if $p \leq q,$} \\
1, & \mbox{if $p \geq q,$} \end{array}\right.
[[/math]]
and
[[math]]
h'(1) = \left \{ \begin{array}{ll}
1/(p - q), & \mbox{if $p \gt q,$}\\
\infty, & \mbox{if $p = q.$} \end{array}\right.
[[/math]]