Stieltjes-Wigert

From DRMF
Jump to navigation Jump to search

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): &