Correction to a theorem of Schoenberg

Mathematics – General Mathematics

Scientific paper

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4 pages

Scientific paper

A well-known theorem of Schoenberg states that if f(z) generates a PF_r
sequence then 1/f(-z) generates a PF_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(z) generates a PF sequence then
1/f(-z) generates a PF sequence.

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