Laguerre polynomials

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In mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834–1886), are nontrivial solutions of Laguerre's differential equation: x y ″ + ( 1 − x ) y ′ + n y = 0 , y = L ( x ) {\displaystyle xy''+(1-x)y'+ny=0,\ y=L(x)} which is a second-order linear differential equation. This equation has nonsingular solutions only if n is a non-negative integer. Sometimes the name Laguerre polynomials is used for solutions of x y ″ + ( α + 1 − x ) y ′ + n y = 0 . {\displaystyle xy''+...

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