Continuous q-Hahn

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Continuous q-Hahn

Basic hypergeometric representation

Substitution(s):


Orthogonality relation(s)

Substitution(s): &

&


Recurrence relation

Substitution(s): &


Monic recurrence relation

Substitution(s): &


q-Difference equation

Substitution(s): &

&
&
&
&


Forward shift operator

Substitution(s):


Backward shift operator

Substitution(s): &

&
&


Substitution(s): &

&
&


Rodrigues-type formula

Substitution(s): &

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Generating functions

Substitution(s):


Substitution(s):


Substitution(s):


Limit relations

Askey-Wilson polynomial to Continuous q-Hahn polynomial


Continuous q-Hahn polynomial to q-Meixner-Pollaczek polynomial


Continuous q-Hahn polynomial to Continuous Hahn polynomial

Remark

Koornwinder Addendum: Continuous q-Hahn