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 formulate and derive a generalization of an orthogonal rational-function basis for spectral expansions over the infinite or semi-infinite interval. The original functions, first presented by Wiener, are a mapping and weighting of the Fourier basis to the infinite interval. By identifying the Fourier series as a biorthogonal composition of Jacobi polynomials/functions, we are able to define generalized Fourier series which, when appropriately mapped to the whole real line and weighted, generalize Wiener's basis functions. It is known that the original Wiener rational functions inherit sparse Galerkin matrices for differentiation, and can utilize the fast Fourier transform (FFT) for computation of the expansion coefficients. We show that the generalized basis sets also have a sparse differentiation matrix and we discuss connection problems, which are necessary theoretical developments for application of the FFT.

A generalization of the Wiener rational basis functions on infinite intervals: Part I–derivation and properties