Laguerre Polynomial Calculator

L_n(x) on [0,∞)

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L_5^(0)(1)

-0.466667

Sequence

n=0L^α=1.0000L⁰=1.0000

n=1L^α=0.0000L⁰=0.0000

n=2L^α=-0.5000L⁰=-0.5000

n=3L^α=-0.6667L⁰=-0.6667

n=4L^α=-0.6250L⁰=-0.6250

n=5L^α=-0.4667L⁰=-0.4667

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About Laguerre Polynomial Calculator

A Laguerre polynomial calculator computing L_n(x) via recurrence (n+1)L_{n+1}=(2n+1-x)L_n−nL_{n-1}. L_0=1, L_1=1−x, L_2=(x²−4x+2)/2. Hydrogen radial wavefunctions use associated Laguerre L_n^α. Client-side.

Laguerre Polynomial Calculator Features

L_n(x) value
Associated L_n^α
Coefficients
Hydrogen atom
Sequence

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