Continuous q-Hermite

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Continuous q-Hermite

Basic hypergeometric representation

Substitution(s):


Orthogonality relation(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): &
arbitrary


Limit relations

Continuous big q-Hermite polynomial to Continuous q-Hermite polynomial


Continuous q-Laguerre polynomial to Continuous q-Hermite polynomial


Continuous q-Hermite polynomial to Hermite polynomial

Remark

Substitution(s):