Formula:KLS:14.15:12

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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \qKrawtchouk{n}@{q^{-x-1}}{p}{N}{q}-\qKrawtchouk{n}@{q^{-x}}{p}{N}{q} {}=\frac{q^{-n-x}(1-q^n)(1+pq^n)}{1-q^{-N}}\qKrawtchouk{n-1}@{q^{-x}}{pq^2}{N-1}{q} }}

Proof

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Symbols List

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle K_{n}}}  : Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}} -Krawtchouk polynomial : http://drmf.wmflabs.org/wiki/Definition:qKrawtchouk

Bibliography

Equation in Section 14.15 of KLS.

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