Laguerre

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Laguerre

Hypergeometric representation

Orthogonality relation(s)

Constraint(s):


Recurrence relation

Monic recurrence relation


Differential equation

Substitution(s):


Forward shift operator

Backward shift operator


Rodrigues-type formula

Generating functions



Constraint(s): arbitrary


Limit relations

Meixner-Pollaczek polynomial to Laguerre polynomial


Jacobi polynomial to Laguerre polynomial


Meixner polynomial to Laguerre polynomial


Laguerre polynomial to Hermite polynomial

Remarks





Koornwinder Addendum: Laguerre

Laguerre: Special value


Quadratic transformations



Fourier transform


Differentiation formulas





Generalized Hermite polynomials