Formula:KLS:14.05:70
Jump to navigation
Jump to search
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle x\monicbigqLegendre{n}@@{x}{c}{q}=\monicbigqLegendre{n+1}@@{x}{c}{q}+\left[1-(A_n+C_n)\right]\monicbigqLegendre{n}@@{x}{c}{q}+A_{n-1}C_n\monicbigqLegendre{n-1}@@{x}{c}{q} }}
Substitution(s)
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle C_n=-cq^{n+1}\frac{(1-q^n)(1-c^{-1}q^n)}{(1+q^n)(1-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+1})(1-cq^{n+1})}{(1+q^{n+1})(1-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+1})(1-cq^{n+1})}{(1+q^{n+1})(1-q^{2n+1})}}}
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 P}_{n}}}
: monic big Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle q}}
-Legendre polynomial : http://drmf.wmflabs.org/wiki/Definition:monicbigqLegendre
Bibliography
Equation in Section 14.5 of KLS.
URL links
We ask users to provide relevant URL links in this space.