The functions (1 - r)- 2|λ | (1 - 2xr + r² )- λ are shown to be absolutely monotonic, or equivalently, that their power series have nonnegative coefficients for - 1 x 1. One consequence is a simple proof of Kogbetliantz’s theorem on positive Cesàro summability for ultraspherical series, [7].
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Askey et al. (1974) studied this question.