Krawtchouk

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Krawtchouk

Hypergeometric representation

Constraint(s):


Orthogonality relation(s)

Constraint(s):


Recurrence relation

Monic recurrence relation


Difference equation

Substitution(s):


Forward shift operator


Backward shift operator


Rodrigues-type formula

Generating functions



Constraint(s): arbitrary


Limit relations

Hahn polynomial to Krawtchouk polynomial


Dual Hahn polynomial to Krawtchouk polynomial


Krawtchouk polynomial to Charlier polynomial


Krawtchouk polynomial to Hermite polynomial

Remarks

Constraint(s):



Koornwinder Addendum: Krawtchouk

Krawtchouk: Special values





Symmetry







Quadratic transformations





Generating functions