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

The theorems relative to finite differences, given by M. Lagrange in the Berlin Memoirs, for 1772, have much engaged the attention of mathematicians. M. Laplace has been particularly successful in his investigations respecting them; yet an important difficulty remained, to endeavour to surmount which is the principal object of this Paper. The theorems alluded to may be thus stated. Letu represent any function ofx . Letx +h ,x +2h ,x +3h , &amp;c. be successive values ofx , and1 u ,2 u ,3 u &amp;c. corresponding successive values ofu . Let Δn u represent the first term of then th order of differences of the quantitiesu ,1 u ,2 u &amp;c. And let also Sn u represent the first term of a series of quantities, of which the first term of then th order of differences isu . Then (e representing the series 1 + 1 + 1/1.2 + 1/1.2.3 +, &amp;c.)

VI. An investigation of the general term of an important series in the inverse method of finite differences