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Showing content from http://reference.wolfram.com/language/guide/FunctionsForSeparableCoordinateSystems.html below:

Functions for Separable Coordinate Systems—Wolfram Language Documentation

Functions for Separable Coordinate Systems—Wolfram Language Documentation WOLFRAM Products

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Sin  ▪  Cos  ▪  Exp

Polar Coordinates

BesselJ  ▪  BesselY  ▪  HankelH2

Elliptical Coordinates

MathieuS  ▪  MathieuC

Spherical Coordinates

SphericalHarmonicY  ▪  LegendreP  ▪  SphericalBesselJ  ▪  SphericalBesselY  ▪  SphericalHankelH2  ▪  LaguerreL

Ultraspherical Coordinates

GegenbauerC  ▪  Hypergeometric2F1

Toroidal Coordinates

LegendreQ  ▪  LegendreP

Spheroidal Coordinates

SpheroidalPS  ▪  SpheroidalS1

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