Big q-Jacobi

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Big q-Jacobi

Basic hypergeometric representation

Orthogonality relation(s)

Recurrence relation

Substitution(s): &


Monic recurrence relation

Substitution(s): &


q-Difference equation

Substitution(s): &

&


Forward shift operator


Backward shift operator


Substitution(s):


Rodrigues-type formula

Substitution(s):


Generating functions


Limit relations

Askey-Wilson polynomial to Big q-Jacobi polynomial



q-Racah polynomial to Big q-Jacobi polynomial


Big q-Jacobi polynomial to Big q-Laguerre polynomial


Big q-Jacobi polynomial to Little q-Jacobi polynomial


Big q-Jacobi polynomial to q-Meixner polynomial


Big q-Jacobi polynomial to Jacobi polynomial


Remarks





Koornwinder Addendum: Big q-Jacobi

Different notation





Orthogonality relation

Substitution(s): &


Substitution(s): &


Other hypergeometric representation and asymptotics






Symmetry


Big q-Jacobi: Special values





Quadratic transformations