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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

In the paper, by virtue of the famous formula of Fa\`a di Bruno, with the aidof several identities of partial Bell polynomials, by means of a formula forderivatives of the ratio of two differentiable functions, and with availabilityof other techniques, the authors establish closed-form formulas in terms of theBernoulli numbers and the second kind Stirling numbers, present determinantalexpressions, derive recursive relations, obtain power series, and computespecial values of the function $\frac{v^j}{1-\operatorname{e}^{-v}}$, itsderivatives, and related ones used in Clark--Ismail's two conjectures. By theseresults, the authors also discover a formula for the determinant of aHessenberg matrix and derive logarithmic convexity of a sequence related to thefunction and its derivatives.

applied and computational mathematics

Closed-form formulas, determinantal expressions, recursive relations,  power series, and special values of several functions used in Clark--Ismail's  two conjectures