Q-Bessel

From DRMF
Jump to navigation Jump to search

q-Bessel

Basic hypergeometric representation



Orthogonality relation(s)

Constraint(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

Constraint(s):


Limit relations

Little q-Jacobi polynomial to q-Bessel polynomial


q-Krawtchouk polynomial to q-Bessel polynomial


q-Bessel polynomial to Stieltjes-Wigert polynomial


q-Bessel polynomial to Bessel polynomial


q-Bessel polynomial to Charlier polynomial

Remark

Reference