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Published online by Cambridge University Press: 20 November 2018
A well-known theorem states that if $f\left( z \right)$ generates a
$\text{P}{{\text{F}}_{r}}$ sequence then
$1/f\left( -z \right)$ generates a
$\text{P}{{\text{F}}_{r}}$ sequence. We give two counterexamples which show that this is not true, and give a correct version of the theorem. In the infinite limit the result is sound: if
$f\left( z \right)$ generates a
$\text{PF}$ sequence then
$1/f\left( -z \right)$ generates a
$\text{PF}$ sequence.