Laguerre Polynomials - Relation To Hermite Polynomials

Relation To Hermite Polynomials

The generalized Laguerre polynomials are related to the Hermite polynomials:

and

where the Hn(x) are the Hermite polynomials based on the weighting function exp(−x2), the so-called "physicist's version."

Because of this, the generalized Laguerre polynomials arise in the treatment of the quantum harmonic oscillator.

Read more about this topic:  Laguerre Polynomials

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