English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We obtain so far unproved properties of a ratio involving a class of Hermiteand parabolic cylinder functions. Those ratios are shown to be strictlydecreasing and bounded by universal constants. Differently to usual analyticapproaches, we employ simple purely probabilistic arguments to derive ourresults. In particular, we exploit the relation between Hermite and paraboliccylinder functions and the eigenfunctions of the infinitesimal generator of theOrnstein-Uhlenbeck process. As a byproduct, we obtain Tur\'an typeinequalities.

Universal Bounds and Monotonicity Properties of Ratios of Hermite and Parabolic Cylinder Functions