Formula:KLS:14.15:04
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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle -\left(1-q^{-x}\right)\qKrawtchouk{n}@@{q^{-x}}{p}{N}{q}=A_n\qKrawtchouk{n+1}@@{q^{-x}}{p}{N}{q}-\left(A_n+C_n\right)\qKrawtchouk{n}@@{q^{-x}}{p}{N}{q} {}+C_n\qKrawtchouk{n-1}@@{q^{-x}}{p}{N}{q} }}
Substitution(s)
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle C_n=-pq^{2n-N-1}\frac{(1+pq^{n+N})(1-q^n)}{(1+pq^{2n-1})(1+pq^{2n})}}}
&
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle A_n=\frac{(1-q^{n-N})(1+pq^n)}{(1+pq^{2n})(1+pq^{2n+1})}}}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle A_n=\frac{(1-q^{n-N})(1+pq^n)}{(1+pq^{2n})(1+pq^{2n+1})}}}
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}}}
: 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.
URL links
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