Q-Laguerre

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q-Laguerre

Basic hypergeometric representation


Orthogonality relation(s)

Constraint(s):


Constraint(s): &


Constraint(s):


Recurrence relation

Monic recurrence relation


q-Difference equation

Substitution(s):


Forward shift operator


Backward shift operator


Substitution(s):


Rodrigues-type formula

Substitution(s):


Generating functions




Constraint(s): arbitrary


Limit relations

Little q-Jacobi polynomial to q-Laguerre polynomial


q-Meixner polynomial to q-Laguerre polynomial


q-Laguerre polynomial to Stieltjes-Wigert polynomial


q-Laguerre polynomial to Laguerre / Charlier polynomial



Remarks



Koornwinder Addendum: q-Laguerre

Orthogonality relation

Substitution(s):


Substitution(s): &


Expansion of x^n


Quadratic transformations