Legendre equation

Legendre equation

[lə′zhän·drə i‚kwā·zhən]
(mathematics)
The second-order linear homogeneous differential equation (1 -x 2) y ″ - 2 xy ′ + v (v + 1) y = 0, where v is real and nonnegative.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
The polar angle dependence 0 leads to the associated Legendre equation
When [alpha] = 1/2, the equation reduces to the Legendre equation, and the Gegenbauer polynomials reduce to the Legendre polynomials.
(15) Associated Legendre equation [Dunford and Schwartz 1963, p.