Legendre's differential equation

proper noun

The equation that defines the Legendre polynomials: d/dx[(1-x²)d/dxP_n(x)]+n(n+1)P_n(x)=0.

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Meanings

proper noun
  1. mathematicsThe equation that defines the Legendre polynomials: d/dx[(1-x²)d/dxP_n(x)]+n(n+1)P_n(x)=0.

Origin

Named after French mathematician Adrien-Marie Legendre (1752–1833).

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Cite this entry
APA

Legendre's differential equation. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/Legendre's%20differential%20equation

MLA

“Legendre's differential equation.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Legendre's%20differential%20equation. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “Legendre's differential equation,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/Legendre's%20differential%20equation.

Source: Legendre's differential equation on Wiktionary, CC BY-SA 4.0.