Sokal, Alan D;
(2022)
When does a hypergeometric function pFq belong to the Laguerre–Pólya class LP⁺?
Journal of Mathematical Analysis and Applications
, 515
(2)
, Article 126432. 10.1016/j.jmaa.2022.126432.
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Abstract
I show that a hypergeometric function p q F (a1, . . . , ap; b1, . . . , bq; ·) with p ≤ q belongs to the Laguerre–P´olya class LP + for arbitrarily large bp+1, . . . , bq > 0 if and only if, after a possible reordering, the differences ai −bi are nonnegative integers. This result arises as an easy corollary of the case p = q proven two decades ago by Ki and Kim. I also give explicit examples for the case 1 2 F .
| Type: | Article |
|---|---|
| Title: | When does a hypergeometric function pFq belong to the Laguerre–Pólya class LP⁺? |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.jmaa.2022.126432 |
| Publisher version: | https://doi.org/10.1016/j.jmaa.2022.126432 |
| Language: | English |
| Additional information: | © 2022 The Author. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). |
| Keywords: | Hypergeometric function, entire function, Laguerre–P´olya class, Stieltjes moment sequence, continued fraction. |
| UCL classification: | UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics UCL > Provost and Vice Provost Offices > UCL BEAMS UCL |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10150527 |
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