On the multiplicities of the zeros of Laguerre-Pólya functions

Kamimoto, Joe; Ki, Haseo; Kim, Young-One

doi:10.1090/s0002-9939-99-04970-9

Cited by 5 publications

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References 11 publications

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“…If φ ∈ LP is not of the form φ(x) = ce γx with c = 0, then it is easy to see that φ(0) = 0 or φ ′′ (0)φ(0) − φ ′ (0) 2 < 0 (for a proof, see [5,9]); hence Theorem B as well as Theorem 1.1 implies that φ has the Pólya-Wiman property with respect to arbitrary real polynomials. On the other hand, there are plenty of formal power series φ with real coefficients which satisfy φ(0) = 0 or φ ′′ (0)φ(0) − φ ′ (0) 2 < 0, but do not represent Laguerre-Pólya functions.…”

Section: Introductionmentioning

confidence: 99%

Department of Chemistry, Seoul National University

Kim

2008

Mol. Sci.

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Section: Introductionmentioning

confidence: 99%