Formula:KLS:14.17:26

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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \lim_{q\rightarrow 1}\dualqKrawtchouk{n}@{\lambda(x)}{1-p^{-1}}{N}{q}=\Krawtchouk{n}@{x}{p}{N} }}

Substitution(s)

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \lambda(n)=q^{-n}-pq^n}} &

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \lambda(x)=q^{-x}+cq^{x-N}}} &
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \lambda(x):=q^{-x}+cq^{x-N}}} &
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \lambda(n)=q^{-n}-pq^n}} &

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \lambda(x)=q^{-x}+cq^{x-N}}}


Proof

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Symbols List

& : logical and
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle K_{n}}}  : dual 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:dualqKrawtchouk
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle K_{n}}}  : Krawtchouk polynomial : http://dlmf.nist.gov/18.19#T1.t1.r6

Bibliography

Equation in Section 14.17 of KLS.

URL links

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