Title: Some Absolutely Monotonic and Completely Monotonic Functions
Abstract: The functions $(1 - r)^{ - 2|\lambda |} (1 - 2xr + r^2 )^{ - \lambda } $ are shown to be absolutely monotonic, or equivalently, that their power series have nonnegative coefficients for $ - 1 \leqq x \leqq 1$. One consequence is a simple proof of Kogbetliantz's theorem on positive Cesàro summability for ultraspherical series, [7].
Publication Year: 1974
Publication Date: 1974-02-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 41
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