Affine q-Krawtchouk

From DRMF
Jump to navigation Jump to search

Affine q-Krawtchouk

Basic hypergeometric representation

Constraint(s):


Orthogonality relation(s)

Constraint(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


Limit relations

q-Hahn polynomial to Affine q-Krawtchouk polynomial


Dual q-Hahn polynomial to Affine q-Krawtchouk polynomial


Affine q-Krawtchouk polynomial to Little q-Laguerre / Wall polynomial


Affine q-Krawtchouk polynomial to Krawtchouk polynomial

Remarks


Koornwinder Addendum: Affine q-Krawtchouk