Formula:KLS:14.06:07
Jump to navigation
Jump to search
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle x\monicqHahn{n}@@{x}{\alpha}{\beta}{N}{q}=\monicqHahn{n+1}@@{x}{\alpha}{\beta}{N}{q}+\left[1-(A_n+C_n)\right]\monicqHahn{n}@@{x}{\alpha}{\beta}{N}{q}+A_{n-1}C_n\monicqHahn{n-1}@@{x}{\alpha}{\beta}{N}{q} }}
Substitution(s)
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle C_n=-\frac{\alpha q^{n-N}(1-q^n)(1-\alpha\beta q^{n+N+1})(1-\beta q^n)}{(1-\alpha\beta q^{2n})(1-\alpha\beta q^{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-\alpha q^{n+1})(1-\alpha\beta q^{n+1})}{(1-\alpha\beta q^{2n+1})(1-\alpha\beta q^{2n+2})}}}
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-\alpha q^{n+1})(1-\alpha\beta q^{n+1})}{(1-\alpha\beta q^{2n+1})(1-\alpha\beta q^{2n+2})}}}
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 {\widehat Q}_{n}}}
: monic Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}}
-Hahn polynomial : http://drmf.wmflabs.org/wiki/Definition:monicqHahn
Bibliography
Equation in Section 14.6 of KLS.
URL links
We ask users to provide relevant URL links in this space.