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]]