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

We show that in the particular case when a characteristic exponent of thesingularity at infinity is zero the solution of the general Heun equation canbe expanded in terms of the incomplete Beta functions. By means of terminationof the series, closed-form solutions are derived for two infinite sets of theinvolved parameters. These finite-sum solutions are written in terms ofelementary functions that in general are quasi-polynomials. The coefficients ofthe expansion obey a three-term recurrence relation, which in some particularcases may become two-term. We discuss the case when the recurrence relationinvolves two non-successive terms and show that the coefficients of theexpansion are then calculated explicitly and the general solution of the Heunequation is constructed as a combination of several hypergeometric functionswith quasi-polynomial pre-factors.

A series solution of the general Heun equation in terms of incomplete Beta functions