Continuous q-Jacobi: Special cases

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Continuous q-Jacobi: Special cases

Continuous q-ultraspherical / Rogers

Basic hypergeometric representation

Substitution(s):



Orthogonality relation(s)

Constraint(s):


Substitution(s): &

&


Recurrence relation

Monic recurrence relation


q-Difference equation

Substitution(s): &

&
&
&
&


Forward shift operator

Substitution(s):


Backward shift operator

Substitution(s): &

&
&


Substitution(s): &

&
&


Rodrigues-type formula

Substitution(s): &

&
&


Generating functions

Substitution(s):


Substitution(s):


Substitution(s):


Substitution(s):


Substitution(s):


Substitution(s):


Substitution(s): &
arbitrary


Limit relations

Askey-Wilson polynomial to Continuous q-ultraspherical / Rogers polynomial


q-Meixner-Pollaczek polynomial to Continuous q-ultraspherical /


Continuous q-ultraspherical / Rogers polynomial to Continuous q-Hermite polynomial


Continuous q-ultraspherical / Rogers polynomial to Gegenbauer /

Remarks

Substitution(s):