CACrown ArchivesThe cinema collection
EN/FR
Search
Menu
Research dossier · General Reference

Spheroidal wave function

Solutions of the Helmholtz equation

Cross-disciplinary reference desk with index cards, atlas, dictionary and catalogue
General referenceInterpretive dossier study · Crown Archives visual atlas
Record originEnglish Wikipedia
Text licenseCC BY-SA 4.0
Source revisionApr 6, 2021
Entity authorityQ7576728 ↗
Source-derived summary

Spheroidal wave functions are solutions of the Helmholtz equation that are found by writing the equation in spheroidal coordinates and applying the technique of separation of variables, just like the use of spherical coordinates lead to spherical harmonics. They are called oblate spheroidal wave functions if oblate spheroidal coordinates are used and prolate spheroidal wave functions if prolate spheroidal coordinates are used.

If instead of the Helmholtz equation, the Laplace equation is solved in spheroidal coordinates using the method of separation of variables, the spheroidal wave functions reduce to the spheroidal harmonics. With oblate spheroidal coordinates, the solutions

are called oblate harmonics and with prolate spheroidal coordinates, prolate harmonics. Both type of spheroidal harmonics

are expressible in terms of Legendre functions.

See also

Oblate spheroidal coordinates, especially the section Oblate spheroidal harmonics, for a more extensive discussion.

Oblate spheroidal wave function

References

Notes

Bibliography

C. Niven On the Conduction of Heat in Ellipsoids of Revolution. Philosophical transactions of the Royal Society of London, v. 171 p. 117 (1880)

M. Abramowitz and I. Stegun, Handbook of Mathematical function (US Gov.

Editorial summary

This brief starts where responsible research should: with the source description of “Spheroidal wave function” as solutions of the Helmholtz equation. Everything that follows is an evidence route, not borrowed authority.

Editorial reviewA dependable orientation record for establishing vocabulary, names and a first evidence trail. The current lead gives the account dated anchors—1880—that can be checked directly. The selected authority fields contribute no independent date. The account is most persuasive where Spheroidal, wave and function can be independently traced.
Editorial analysis

Why this record matters

The subject matters to the general reference register because the source frames it as solutions of the Helmholtz equation. Its deeper value depends on whether names, dates, institutions and citations support that framing.

Evidence profile

Named sources, stable identifiers and responsible institutions provide the strongest route from overview to verifiable evidence. The source revision retrieved here is dated Apr 6, 2021. The linked authority identifier is Q7576728. None of the 0 selected statements returned an explicit reference. The first chronological checks are 1880.

Critical limits

The absence of detail may reflect summary conventions rather than a lack of surviving documentation. The lead is largely declarative, so disagreement and counter-evidence require a deliberate search beyond the opening account. Authority statements aid reconciliation but still require their own references, qualifiers and ranks to be checked.

How to read it

Use the entry as an orientation point, then follow its citations and revision history. Names, dates and institutional relationships should be checked against the original record.

Best used for
  • Subject orientation
  • Search vocabulary
  • Locating named sources
Verify next

The closest primary source, responsible institution and strongest cited specialist reference.

Three-step research path

  1. Establish the record: confirm the title “Spheroidal wave function”, its source revision and the description used here.
  2. Expand the search: follow Spheroidal wave function primary sources, Spheroidal wave function archive and Spheroidal research across catalogues and specialist indexes.
  3. Test the account: compare the strongest cited source with the responsible institution’s current record and note any disagreement.

Questions for further research

  1. Which source most directly establishes the central claim about “Spheroidal wave function”?
  2. What terminology or title could unlock a more precise catalogue search?
  3. Which cited source is closest to the event, object or claim?
Subject index

Search terms from this dossier

Source & attribution

This entry incorporates text from “Spheroidal wave function” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.