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/

Zendy Plus

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

Zendy Tools

Zendy Open

We prove the existence of stationary random fields with linear regressionsfor $q>1$ and thus close an open question posed by W. Bryc et al.. We provethis result by describing a discrete 1 dimensional conditional distribution andthen checking Chapman-Kolmogorov equation. Support of this distribution consistof zeros of certain Al-Salam-Chihara polynomials. To find them we refer to andexpose known result concerning addition of $q-$ exponential function. Thisleads to generalization of a well known formula $(x+y)^{n}%=\sum_{i=0}^{n}\binom{n}{k}i^{k}H_{n-k}(x) H_{k}(-iy) ,$ where $H_{k}(x) $denotes $k-$th Hermite polynomial.

Probabilistic implications of symmetries of q-Hermite and Al-Salam-Chihara polynomials