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Mathieu function — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Mathieu_function
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-06T18:06:58.562Z
SHA-256 of the archived text: 8389b4c5e61d131860d8819d7394f79b1842b1fb02ee4e2bc05479866f545a78
Stable URL of this page: https://metraipolis.com/documento/dc_5097dacc2dfd

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Mathieu function — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Mathieu_function (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_5097dacc2dfd (Metraipolis archive dc_5097dacc2dfd, sha256 8389b4c5e61d131860d8819d7394f79b1842b1fb02ee4e2bc05479866f545a78)

BibTeX

@misc{dc5097dacc2dfd,
  title = {Mathieu function — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Mathieu_function},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_5097dacc2dfd; sha256 8389b4c5e61d131860d8819d7394f79b1842b1fb02ee4e2bc05479866f545a78},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Mathieu_function. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In mathematics, Mathieu functions, sometimes called angular Mathieu functions, are solutions of Mathieu's differential equation d 2 y d x 2 + ( a − 2 q cos ( 2 x ) ) y = 0 , {\displaystyle {\frac {d^{2}y}{dx^{2}}}+(a-2q\cos(2x))y=0,} where a, q are real-valued parameters. Since we may add π/2 to x to change the sign of q, it is a usual convention to set q ≥ 0. They were first introduced by Émile Léonard Mathieu, who encountered them while studying vibrating elliptical drumheads. They have applications in many fields of the physical sciences, such as optics, quantum mechanics, and general relativity. They tend to occur in problems involving periodic motion, or in the analysis of partial differential equation (PDE) boundary value problems possessing elliptic symmetry.

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; ricerca «differential equation»).
Fonte: Wikipedia in inglese, voce «Mathieu function» — https://en.wikipedia.org/wiki/Mathieu_function
Wikidata Q1908689 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q1908689
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Mathieu_function?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1368695531, consultata il 2026-10-06T16:32:14.383Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 287457e4f118896a13634283598b318448fa0cef91bf0bc440a1ebf28026858f