Formula:KLS:14.15:17

<< Formula:KLS:14.15:15

formula in q-Krawtchouk

Formula:KLS:14.15:18 >>

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

Substitution(s)

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle w(x;p,N;q)=\frac{\qPochhammer{q^{-N}}{q}{x}}{\qPochhammer{q}{q}{x}}\left(-\frac{q}{p}\right)^x}}

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
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle (a;q)_n}}  : Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}} -Pochhammer symbol : http://dlmf.nist.gov/5.18#i http://dlmf.nist.gov/17.2#SS1.p1

Bibliography

Equation in Section 14.15 of KLS.

URL links

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<< Formula:KLS:14.15:15

formula in q-Krawtchouk

Formula:KLS:14.15:18 >>