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

In this paper are discussed the results of new numerical experiments on zerodistribution of type I Hermite-Pad\'e polynomials of order $n=200$ for threedifferent collections of three functions $[1,f_1,f_2]$. These results areobtained by the authors numerically and do not match any of the theoreticalresults that were proven so far. We consider three simple cases of multivaluedanalytic functions $f_1$ and $f_2$, with separated pairs of branch pointsbelonging to the real line. In the first case both functions have twologarithmic branch points, in the second case they both have branch points ofsecond order, and finally, in the third case they both have branch points ofthird order.  All three cases may be considered as representative of the asymptotic theoryof Hermite-Pad\'e polynomials. In the first two cases the numerical zerodistribution of type I Hermite-Pad\'e polynomials are similar to each other,despite the different kind of branching. But neither the logarithmic case, northe square root case can be explained from the asymptotic point of view of thetheory of type I Hermite-Pad\'e polynomials.  The numerical results of the current paper might be considered as a challengefor the community of all experts on Hermite-Pad\'e polynomials theory.

On the limit zero distribution of type I Hermite-Pad\'e polynomials