The Newton Polyhedron and Positivity of $${}_2F_3$$ Hypergeometric Functions

Cho, Yong-Kum; Chung, Seok-Young

doi:10.1007/s00365-021-09540-7

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2021

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“…We should remark that these results not only extend Williamson's positivity result for α = 3 but also disprove his conjecture that there exists α with 2 < α < 3 such that Ψ α (x) remains nonnegative for α ≥ α but changes sign for 0 < α < α (see also [2]).…”

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confidence: 67%

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The zeros of certain Fourier transforms:Improvements of Pólya's results

Cho,

Park

2021

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As for the Fourier transforms of positive and integrable functions supported in the unit interval, we make a list of improvements for Pólya's results on the distribution of their positive zeros and give new sufficient conditions under which those zeros are simple and regularly distributed. As an application, we take the two-parameter family of beta probability density functions defined bywhere α > 0, β > 0, and specify the distribution of zeros of the associated Fourier transforms for some region of (α, β) in the first quadrant which turns out to be much larger than the region where Pólya's results are applicable.

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confidence: 67%

“…In the recent work [2], Cho and Chung investigated the positivity problem for the general 2 F 3 hypergeometric function of the form…”

Section: Main Applicationsmentioning

confidence: 99%