Al-Salam-Chihara

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Al-Salam-Chihara

Basic hypergeometric representation

Substitution(s):



Orthogonality relation(s)

Substitution(s): &

&


Substitution(s): &

&
&
&


Recurrence relation


Monic recurrence relation


q-Difference equation

Substitution(s): &

&
&
&



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): &
arbitrary


Limit relations

Continuous dual q-Hahn polynomial to Al-Salam-Chihara polynomial


Al-Salam-Chihara polynomial to Continuous big q-Hermite polynomial


Al-Salam-Chihara polynomial to Continuous q-Laguerre polynomial


Al-Salam-Chihara polynomial to Meixner-Pollaczek polynomial

Koornwinder Addendum: Al-Salam-Chihara

Re: (14.8.1)




Orthogonality


Normalized recurrence relation