Formula:KLS:14.17:16

<< Formula:KLS:14.17:15

formula in Dual q-Krawtchouk

Formula:KLS:14.17:17 >>

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

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

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

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

Bibliography

Equation in Section 14.17 of KLS.

URL links

We ask users to provide relevant URL links in this space.

<< Formula:KLS:14.17:15

formula in Dual q-Krawtchouk

Formula:KLS:14.17:17 >>