Distributional Weber transformation

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 1981Publisher:Biodiversity Heritage LibraryJournal:Journal and proceedings of the Royal Society of New South Wales, volume 114, pages 63-75 (issn: 0035-9173,

Copyright policy )

Authors: Pathak, R S; Pandey, R K;

doi: 10.5962/p.361140

Distributional Weber transformation

- Summary
- Subjects
- Metrics

Abstract

The classical Weber transformation \[ F(u)=\int_a^\infty t[J_\nu(tu)Y_\nu(au)-J_\nu(au)Y_\nu(tu)] f(\tau)\,d\tau \] is extended to a class of generalized functions. An inversion formula is obtained and some applications are given. Notice that in equation (8) the lower limit for \(t\)-integral should be \(a\), and in equation (41), and in all others following it, \(\nu\) should be zero.

Keywords

Source: Biodiversity Heritage Library, inversion formula, Source: BHL, Integral transforms in distribution spaces, Weber transformation, Biodiversity, BHL-Corpus, Special integral transforms (Legendre, Hilbert, etc.), Source: https://biodiversitylibrary.org

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	1
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average

Found an issue? Give us feedback

1

Average

Green