KnowraLegendre polynomialsLinked fromLinked fromThe 9 pages that link to Legendre polynomials, each with the reason it gives.All 9Broader topic 5Related 1Narrower topic 1Compared with 2Spherical harmonicsNarrower topic: The zero-order spherical harmonics reduce to Legendre polynomials of the polar angle’s cosine.Adrien-Marie LegendreBroader topic: Their role in potential theory extends Legendre’s mathematical-physics research.Chebyshev polynomialsCompared with: They share the interval but use a different weight from Chebyshev polynomials.Multipole expansionRelated: They appear in the axisymmetric expansion of inverse-distance potentials.Fourier coefficientCompared with: Legendre expansions use orthogonal polynomial coefficients rather than oscillatory frequency components.Sturm–Liouville theoryBroader topic: They arise as eigenfunctions for a Sturm–Liouville problem on an interval.Even and odd functionsBroader topic: Each polynomial has definite parity, simplifying expansions on symmetric intervals.Askey–Gasper inequalityBroader topic: They are a simpler classical orthogonal family, while the inequality requires a more specialized Jacobi-polynomial sum.Legendre equationBroader topic: They are the polynomial solutions selected by integer degree.