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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

It is well known that the interpolation error for    $$\left| x\right| ^{\alpha },\alpha &gt;0$$  x α , α &gt; 0 in    $$L_{\infty }\left[ -1,1\right] $$  L ∞ - 1 , 1 by Lagrange interpolation polynomials based on the zeros of the Chebyshev polynomials of first kind can be represented in its limiting form by entire functions of exponential type. In this paper, we establish new asymptotic bounds for these quantities when    $$\alpha $$  α tends to infinity. Moreover, we present some explicit constructions for near best approximation polynomials to    $$\left| x\right| ^{\alpha },\alpha &gt;0$$  x α , α &gt; 0 in the    $$L_{\infty }$$  L ∞ norm which are based on the Chebyshev interpolation process. The resulting formulas possibly indicate a general approach towards the structure of the associated Bernstein constants.

Asymptotics of Polynomial Interpolation and the Bernstein Constants