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

We list some explicit calculations related to a theorem of Clausen originallypublished in 1828, more commonly known as the result that describes the linearthird order differential equation satisfied by the squares and the product ofany two solutions of a linear second order differential equation in the realdomain. The case of the cube of a solution dates to Appell, 1880. Although notcommonly known and perhaps even new to some extent we show that the fourth andfifth powers of such solutions actually satisfy a linear differential equationof order five and six respectively provided the coefficients are sufficientlysmooth. Indeed, it is the case that given any solution of a linear second orderequation its m-th power satisfies an effectively computable linear differentialequation of order m+1.

Remarks on an 1828 theorem of Clausen