Stieltjes-Wigert

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Stieltjes-Wigert

Basic hypergeometric representation

Orthogonality relation(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

q-Laguerre polynomial to Stieltjes-Wigert polynomial


q-Bessel polynomial to Stieltjes-Wigert polynomial


q-Charlier polynomial to Stieltjes-Wigert polynomial


Stieltjes-Wigert polynomial to Hermite polynomial

Remark

Koornwinder Addendum: Stieltjes-Wigert

An alternative weight function

Substitution(s): &