drmf-kls9.ocd
Symbols in KLS Chapter 9
Section 9.1 Wilson
normWilsonWtilde
Occurences: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\Wilson{n}@{x^{2}}{a}{b}{c}{d}=:(-1)^{n}\pochhammer{n+a+b+c+d-1}{n}\monicWilson{n}@{x^{2}}{a}{b}{c}{d}.}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\normWilsonWtilde{n}@{x^{2}}{a}{b}{c}{d}:=\frac{\Wilson{n}@{x^{2}}{a}{b}{c}{d}}{\pochhammer{a+b}{n}\pochhammer{a+c}{n}\pochhammer{a+d}{n}}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\Wilson{n}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\Wilson{n}@{x}{a}{b}{c}{d}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\frac{\Wilson{n}@{x^{2}}{a}{b}{c}{d}}{\pochhammer{a+b}{n}\pochhammer{a+c}{n}\pochhammer{a+d}{n}}{}:=\HyperpFq{4}{3}@{-n,n+a+b+c+d-1,a+ix,a-ix}{a+b,a+c,a+d}{1}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\lim_{q\rightarrow 1}\frac{\AskeyWilson{n}@{\frac{1}{2}\left(q^{ix}+q^{-ix}\right)}{q^{a}}{q^{b}}{q^{c}}{q^{d}}{q}}{(1-q)^{3n}}=\Wilson{n}@{x^{2}}{a}{b}{c}{d}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\lim_{q\rightarrow 1}\frac{\AskeyWilson{n}@{\frac{1}{2}\left(q^{ix}+q^{-ix}\right)}{q^{a}}{q^{b}}{q^{c}}{q^{d}}{q}}{(1-q)^{3n}}=\Wilson{n}@{x^{2}}{a}{b}{c}{d}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\frac{\Wilson{n}@{x^{2}}{a}{b}{c}{d}}{\pochhammer{a+b}{n}\pochhammer{a+c}{n}\pochhammer{a+d}{n}}{}=\HyperpFq{4}{3}@{-n,n+a+b+c+d-1,a+ix,a-ix}{a+b,a+c,a+d}{1}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\frac{1}{2\pi}\int_{0}^{\infty}\left|\frac{\EulerGamma@{a+ix}\EulerGamma@{b+ix}\EulerGamma@{c+ix}\EulerGamma@{d+ix}}{\EulerGamma@{2ix}}\right|^{2}{}\Wilson{m}@{x^{2}}{a}{b}{c}{d}\Wilson{n}@{x^{2}}{a}{b}{c}{d}\,dx{}=\frac{\EulerGamma@{n+a+b}\cdots\EulerGamma@{n+c+d}}{\EulerGamma@{2n+a+b+c+d}}\pochhammer{n+a+b+c+d-1}{n}n!\,\Kronecker{m}{n}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\frac{1}{2\pi}\int_{0}^{\infty}\left|\frac{\EulerGamma@{a+ix}\EulerGamma@{b+ix}\EulerGamma@{c+ix}\EulerGamma@{d+ix}}{\EulerGamma@{2ix}}\right|^{2}{}\Wilson{m}@{x^{2}}{a}{b}{c}{d}\Wilson{n}@{x^{2}}{a}{b}{c}{d}\,dx{}+\frac{\EulerGamma@{a+b}\EulerGamma@{a+c}\EulerGamma@{a+d}\EulerGamma@{b-a}\EulerGamma@{c-a}\EulerGamma@{d-a}}{\EulerGamma@{-2a}}{}\sum_{\begin{array}[]{c}{\scriptstyle k=0,1,2\ldots}\\ {\scriptstyle a+k<0}\end{array}}\frac{\pochhammer{2a}{k}\pochhammer{a+1}{k}\pochhammer{a+b}{k}\pochhammer{a+c}{k}\pochhammer{a+d}{k}}{\pochhammer{a}{k}\pochhammer{a-b+1}{k}\pochhammer{a-c+1}{k}\pochhammer{a-d+1}{k}k!}{}\Wilson{m}@{-(a+k)^{2}}{a}{b}{c}{d}\Wilson{n}@{-(a+k)^{2}}{a}{b}{c}{d}{}=\frac{\EulerGamma@{n+a+b}\cdots\EulerGamma@{n+c+d}}{\EulerGamma@{2n+a+b+c+d}}\pochhammer{n+a+b+c+d-1}{n}n!\,\Kronecker{m}{n}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\normWilsonWtilde{n}@{x^{2}}{a}{b}{c}{d}:=\normWilsonWtilde{n}@{x^{2}}{a}{b}{c}{d}=\frac{\Wilson{n}@{x^{2}}{a}{b}{c}{d}}{\pochhammer{a+b}{n}\pochhammer{a+c}{n}\pochhammer{a+d}{n}}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\Wilson{n}@{x^{2}}{a}{b}{c}{d}=(-1)^{n}\pochhammer{n+a+b+c+d-1}{n}\monicWilson{n}@{x^{2}}{a}{b}{c}{d}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\Wilson{n}@{(x+\textstyle\frac{1}{2}i)^{2}}{a}{b}{c}{d}-\Wilson{n}@{(x-\textstyle\frac{1}{2}i)^{2}}{a}{b}{c}{d}{}=-2inx(n+a+b+c+d-1)\Wilson{n-1}@{x^{2}}{a+\textstyle\frac{1}{2}}{b+\textstyle\frac{1}{2}}{c+\textstyle\frac{1}{2}}{d+\textstyle\frac{1}{2}}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\frac{\delta\Wilson{n}@{x^{2}}{a}{b}{c}{d}}{\delta x^{2}}{}=-n(n+a+b+c+d-1)\Wilson{n-1}@{x^{2}}{a+\textstyle\frac{1}{2}}{b+\textstyle\frac{1}{2}}{c+\textstyle\frac{1}{2}}{d+\textstyle\frac{1}{2}}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{(a-\textstyle\frac{1}{2}-ix)(b-\textstyle\frac{1}{2}-ix)(c-\textstyle\frac{1}{2}-ix)(d-\textstyle\frac{1}{2}-ix)\Wilson{n}@{(x+\textstyle\frac{1}{2}i)^{2}}{a}{b}{c}{d}{}-(a-\textstyle\frac{1}{2}+ix)(b-\textstyle\frac{1}{2}+ix)(c-\textstyle\frac{1}{2}+ix)(d-\textstyle\frac{1}{2}+ix)\Wilson{n}@{(x-\textstyle\frac{1}{2}i)^{2}}{a}{b}{c}{d}{}=-2ix\Wilson{n+1}@{x^{2}}{a-\textstyle\frac{1}{2}}{b-\textstyle\frac{1}{2}}{c-\textstyle\frac{1}{2}}{d-\textstyle\frac{1}{2}}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\frac{\delta\left[\omega(x;a,b,c,d)\Wilson{n}@{x^{2}}{a}{b}{c}{d}\right]}{\delta x^{2}}{}=\omega(x;a-\textstyle\frac{1}{2},b-\textstyle\frac{1}{2}c-\textstyle\frac{1}{2},d-\textstyle\frac{1}{2})\Wilson{n+1}@{x^{2}}{a-\textstyle\frac{1}{2}}{b-\textstyle\frac{1}{2}}{c-\textstyle\frac{1}{2}}{d-\textstyle\frac{1}{2}}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\omega(x;a,b,c,d)\Wilson{n}@{x^{2}}{a}{b}{c}{d}{}=\left(\frac{\delta}{\delta x^{2}}\right)^{n}\left[\omega(x;a+\textstyle\frac{1}{2}n,b+\textstyle\frac{1}{2}nc+\textstyle\frac{1}{2}n,d+\textstyle\frac{1}{2}n)\right]}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\HyperpFq{2}{1}@{a+ix,b+ix}{a+b}{t}\,\HyperpFq{2}{1}@{c-ix,d-ix}{c+d}{t}=\sum_{n=0}^{\infty}\frac{\Wilson{n}@{x^{2}}{a}{b}{c}{d}t^{n}}{\pochhammer{a+b}{n}\pochhammer{c+d}{n}n!}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\HyperpFq{2}{1}@{a+ix,c+ix}{a+c}{t}\,\HyperpFq{2}{1}@{b-ix,d-ix}{b+d}{t}=\sum_{n=0}^{\infty}\frac{\Wilson{n}@{x^{2}}{a}{b}{c}{d}t^{n}}{\pochhammer{a+c}{n}\pochhammer{b+d}{n}n!}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\HyperpFq{2}{1}@{a+ix,d+ix}{a+d}{t}\,\HyperpFq{2}{1}@{b-ix,c-ix}{b+c}{t}=\sum_{n=0}^{\infty}\frac{\Wilson{n}@{x^{2}}{a}{b}{c}{d}t^{n}}{\pochhammer{a+d}{n}\pochhammer{b+c}{n}n!}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{(1-t)^{1-a-b-c-d}{}\HyperpFq{4}{3}@{\frac{1}{2}(a+b+c+d-1),\frac{1}{2}(a+b+c+d),a+ix,a-ix}{a+b,a+c,a+d}{-\frac{4t}{(1-t)^{2}}}{}=\sum_{n=0}^{\infty}\frac{\pochhammer{a+b+c+d-1}{n}}{\pochhammer{a+b}{n}\pochhammer{a+c}{n}\pochhammer{a+d}{n}n!}\Wilson{n}@{x^{2}}{a}{b}{c}{d}t^{n}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\lim_{d\rightarrow\infty}\frac{\Wilson{n}@{x^{2}}{a}{b}{c}{d}}{\pochhammer{a+d}{n}}=\ctsdualHahn{n}@{x^{2}}{a}{b}{c}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\lim_{t\rightarrow\infty}\frac{\Wilson{n}@{(x+t)^{2}}{a-it}{b-it}{c+it}{d+it}}{(-2t)^{n}n!}=\ctsHahn{n}@{x}{a}{b}{c}{d}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\lim_{t\rightarrow\infty}\frac{\Wilson{n}@{\frac{1}{2}(1-x)t^{2}}{\frac{1}{2}(\alpha+1)}{\frac{1}{2}(\alpha+1)}{\frac{1}{2}(\beta+1)+it}{\frac{1}{2}(\beta+1}-it)}{t^{2n}n!}{}=\Jacobi{\alpha}{\beta}{n}@{x}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\normWilsonWtilde{n}@{x^{2}}{a}{b}{c}{d}=\frac{\Wilson{n}@{x^{2}}{a}{b}{c}{d}}{\pochhammer{a+b}{n}\pochhammer{a+c}{n}\pochhammer{a+d}{n}}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\Wilson{n}@{x^{2}}{a}{b}{c}{d}=\frac{\pochhammer{a-ix}{n}\pochhammer{b-ix}{n}\pochhammer{c-ix}{n}\pochhammer{d-ix}{n}}{\pochhammer{-2ix}{n}}\HyperpFq{7}{6}@{2ix-n,ix-\frac{1}{2}n+1,a+ix,b+ix,c+ix,d+ix,-n}{ix-\frac{1}{2}n,1-n-a+ix,1-n-b+ix,1-n-c+ix,1-n-d+ix}{1}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\Wilson{n}@{-a^{2}}{a}{b}{c}{d}=\pochhammer{a+b}{n}\pochhammer{a+c}{n}\pochhammer{a+d}{n}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\frac{|\Wilson{n}@{-a^{2}}{a}{b}{c}{d}|^{2}}{h_{n}}=O(n^{4\realpart{a}-1})\hbox{as $n\to\infty$.}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{ y(x)=\Wilson{n}@{x^{2}}{a}{b}{c}{d}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\Racah{n}@{\lambda(-a+ix)}{a+b-1}{c+d-1}{a+d-1}{a-d}{}=\frac{\Wilson{n}@{x^{2}}{a}{b}{c}{d}}{\pochhammer{a+b}{n}\pochhammer{a+c}{n}\pochhammer{a+d}{n}}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\Racah{n}@{x(x-N+\delta)}{\alpha}{\beta}{-N-1}{\delta}=\frac{\Wilson{n}@{-(x+\frac{1}{2}(\delta-N))^{2}}{\frac{1}{2}(\delta-N)}{\alpha+1-\frac{1}{2}(\delta-N)}{\beta+\frac{1}{2}(\delta+N)+1}{-\frac{1}{2}(\delta+N)}}{\pochhammer{\alpha+1}{n}\pochhammer{\beta+\delta+1}{n}\pochhammer{-N}{n}}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\lim_{d\rightarrow\infty}\frac{\Wilson{n}@{x^{2}}{a}{b}{c}{d}}{\pochhammer{a+d}{n}}=\ctsdualHahn{n}@{x^{2}}{a}{b}{c}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\lim_{t\rightarrow\infty}\frac{\Wilson{n}@{(x+t)^{2}}{a-it}{b-it}{c+it}{d+it}}{(-2t)^{n}n!}=\ctsHahn{n}@{x}{a}{b}{c}{d}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\lim_{t\rightarrow\infty}\frac{\Wilson{n}@{\frac{1}{2}(1-x)t^{2}}{\frac{1}{2}(\alpha+1)}{\frac{1}{2}(\alpha+1)}{\frac{1}{2}(\beta+1)+it}{\frac{1}{2}(\beta+1}-it)}{t^{2n}n!}=\Jacobi{\alpha}{\beta}{n}@{x}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\frac{\Wilson{n}@{x^{2}}{a}{b}{c}{d}}{\pochhammer{a+b}{n}\pochhammer{a+c}{n}\pochhammer{a+d}{n}}{}=\HyperpFq{4}{3}@{-n,n+a+b+c+d-1,a+ix,a-ix}{a+b,a+c,a+d}{1}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\frac{1}{2\pi}\int_{0}^{\infty}\left|\frac{\EulerGamma@{a+ix}\EulerGamma@{b+ix}\EulerGamma@{c+ix}\EulerGamma@{d+ix}}{\EulerGamma@{2ix}}\right|^{2}{}\Wilson{m}@{x^{2}}{a}{b}{c}{d}\Wilson{n}@{x^{2}}{a}{b}{c}{d}\,dx{}=\frac{\EulerGamma@{n+a+b}\cdots\EulerGamma@{n+c+d}}{\EulerGamma@{2n+a+b+c+d}}\pochhammer{n+a+b+c+d-1}{n}n!\,\Kronecker{m}{n}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\frac{1}{2\pi}\int_{0}^{\infty}\left|\frac{\EulerGamma@{a+ix}\EulerGamma@{b+ix}\EulerGamma@{c+ix}\EulerGamma@{d+ix}}{\EulerGamma@{2ix}}\right|^{2}{}\Wilson{m}@{x^{2}}{a}{b}{c}{d}\Wilson{n}@{x^{2}}{a}{b}{c}{d}\,dx{}+\frac{\EulerGamma@{a+b}\EulerGamma@{a+c}\EulerGamma@{a+d}\EulerGamma@{b-a}\EulerGamma@{c-a}\EulerGamma@{d-a}}{\EulerGamma@{-2a}}{}\sum_{\begin{array}[]{c}{\scriptstyle k=0,1,2\ldots}\\ {\scriptstyle a+k<0}\end{array}}\frac{\pochhammer{2a}{k}\pochhammer{a+1}{k}\pochhammer{a+b}{k}\pochhammer{a+c}{k}\pochhammer{a+d}{k}}{\pochhammer{a}{k}\pochhammer{a-b+1}{k}\pochhammer{a-c+1}{k}\pochhammer{a-d+1}{k}k!}{}\Wilson{m}@{-(a+k)^{2}}{a}{b}{c}{d}\Wilson{n}@{-(a+k)^{2}}{a}{b}{c}{d}{}=\frac{\EulerGamma@{n+a+b}\cdots\EulerGamma@{n+c+d}}{\EulerGamma@{2n+a+b+c+d}}\pochhammer{n+a+b+c+d-1}{n}n!\,\Kronecker{m}{n}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\normWilsonWtilde{n}@{x^{2}}{a}{b}{c}{d}:=\normWilsonWtilde{n}@{x^{2}}{a}{b}{c}{d}=\frac{\Wilson{n}@{x^{2}}{a}{b}{c}{d}}{\pochhammer{a+b}{n}\pochhammer{a+c}{n}\pochhammer{a+d}{n}}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\Wilson{n}@{x^{2}}{a}{b}{c}{d}=(-1)^{n}\pochhammer{n+a+b+c+d-1}{n}\monicWilson{n}@{x^{2}}{a}{b}{c}{d}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{ y(x)=\Wilson{n}@{x^{2}}{a}{b}{c}{d}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\Wilson{n}@{(x+\textstyle\frac{1}{2}i)^{2}}{a}{b}{c}{d}-\Wilson{n}@{(x-\textstyle\frac{1}{2}i)^{2}}{a}{b}{c}{d}{}=-2inx(n+a+b+c+d-1)\Wilson{n-1}@{x^{2}}{a+\textstyle\frac{1}{2}}{b+\textstyle\frac{1}{2}}{c+\textstyle\frac{1}{2}}{d+\textstyle\frac{1}{2}}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\frac{\delta\Wilson{n}@{x^{2}}{a}{b}{c}{d}}{\delta x^{2}}{}=-n(n+a+b+c+d-1)\Wilson{n-1}@{x^{2}}{a+\textstyle\frac{1}{2}}{b+\textstyle\frac{1}{2}}{c+\textstyle\frac{1}{2}}{d+\textstyle\frac{1}{2}}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{(a-\textstyle\frac{1}{2}-ix)(b-\textstyle\frac{1}{2}-ix)(c-\textstyle\frac{1}{2}-ix)(d-\textstyle\frac{1}{2}-ix)\Wilson{n}@{(x+\textstyle\frac{1}{2}i)^{2}}{a}{b}{c}{d}{}-(a-\textstyle\frac{1}{2}+ix)(b-\textstyle\frac{1}{2}+ix)(c-\textstyle\frac{1}{2}+ix)(d-\textstyle\frac{1}{2}+ix)\Wilson{n}@{(x-\textstyle\frac{1}{2}i)^{2}}{a}{b}{c}{d}{}=-2ix\Wilson{n+1}@{x^{2}}{a-\textstyle\frac{1}{2}}{b-\textstyle\frac{1}{2}}{c-\textstyle\frac{1}{2}}{d-\textstyle\frac{1}{2}}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\frac{\delta\left[\omega(x;a,b,c,d)\Wilson{n}@{x^{2}}{a}{b}{c}{d}\right]}{\delta x^{2}}{}=\omega(x;a-\textstyle\frac{1}{2},b-\textstyle\frac{1}{2}c-\textstyle\frac{1}{2},d-\textstyle\frac{1}{2})\Wilson{n+1}@{x^{2}}{a-\textstyle\frac{1}{2}}{b-\textstyle\frac{1}{2}}{c-\textstyle\frac{1}{2}}{d-\textstyle\frac{1}{2}}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\omega(x;a,b,c,d)\Wilson{n}@{x^{2}}{a}{b}{c}{d}{}=\left(\frac{\delta}{\delta x^{2}}\right)^{n}\left[\omega(x;a+\textstyle\frac{1}{2}n,b+\textstyle\frac{1}{2}nc+\textstyle\frac{1}{2}n,d+\textstyle\frac{1}{2}n)\right]}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\HyperpFq{2}{1}@{a+ix,b+ix}{a+b}{t}\,\HyperpFq{2}{1}@{c-ix,d-ix}{c+d}{t}=\sum_{n=0}^{\infty}\frac{\Wilson{n}@{x^{2}}{a}{b}{c}{d}t^{n}}{\pochhammer{a+b}{n}\pochhammer{c+d}{n}n!}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\HyperpFq{2}{1}@{a+ix,c+ix}{a+c}{t}\,\HyperpFq{2}{1}@{b-ix,d-ix}{b+d}{t}=\sum_{n=0}^{\infty}\frac{\Wilson{n}@{x^{2}}{a}{b}{c}{d}t^{n}}{\pochhammer{a+c}{n}\pochhammer{b+d}{n}n!}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\HyperpFq{2}{1}@{a+ix,d+ix}{a+d}{t}\,\HyperpFq{2}{1}@{b-ix,c-ix}{b+c}{t}=\sum_{n=0}^{\infty}\frac{\Wilson{n}@{x^{2}}{a}{b}{c}{d}t^{n}}{\pochhammer{a+d}{n}\pochhammer{b+c}{n}n!}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{(1-t)^{1-a-b-c-d}{}\HyperpFq{4}{3}@{\frac{1}{2}(a+b+c+d-1),\frac{1}{2}(a+b+c+d),a+ix,a-ix}{a+b,a+c,a+d}{-\frac{4t}{(1-t)^{2}}}{}=\sum_{n=0}^{\infty}\frac{\pochhammer{a+b+c+d-1}{n}}{\pochhammer{a+b}{n}\pochhammer{a+c}{n}\pochhammer{a+d}{n}n!}\Wilson{n}@{x^{2}}{a}{b}{c}{d}t^{n}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\lim_{d\rightarrow\infty}\frac{\Wilson{n}@{x^{2}}{a}{b}{c}{d}}{\pochhammer{a+d}{n}}=\ctsdualHahn{n}@{x^{2}}{a}{b}{c}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\lim_{t\rightarrow\infty}\frac{\Wilson{n}@{(x+t)^{2}}{a-it}{b-it}{c+it}{d+it}}{(-2t)^{n}n!}=\ctsHahn{n}@{x}{a}{b}{c}{d}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\lim_{t\rightarrow\infty}\frac{\Wilson{n}@{\frac{1}{2}(1-x)t^{2}}{\frac{1}{2}(\alpha+1)}{\frac{1}{2}(\alpha+1)}{\frac{1}{2}(\beta+1)+it}{\frac{1}{2}(\beta+1}-it)}{t^{2n}n!}{}=\Jacobi{\alpha}{\beta}{n}@{x}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\normWilsonWtilde{n}@{x^{2}}{a}{b}{c}{d}=\frac{\Wilson{n}@{x^{2}}{a}{b}{c}{d}}{\pochhammer{a+b}{n}\pochhammer{a+c}{n}\pochhammer{a+d}{n}}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\Wilson{n}@{x^{2}}{a}{b}{c}{d}=\frac{\pochhammer{a-ix}{n}\pochhammer{b-ix}{n}\pochhammer{c-ix}{n}\pochhammer{d-ix}{n}}{\pochhammer{-2ix}{n}}\HyperpFq{7}{6}@{2ix-n,ix-\frac{1}{2}n+1,a+ix,b+ix,c+ix,d+ix,-n}{ix-\frac{1}{2}n,1-n-a+ix,1-n-b+ix,1-n-c+ix,1-n-d+ix}{1}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\Wilson{n}@{-a^{2}}{a}{b}{c}{d}=\pochhammer{a+b}{n}\pochhammer{a+c}{n}\pochhammer{a+d}{n}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\frac{|\Wilson{n}@{-a^{2}}{a}{b}{c}{d}|^{2}}{h_{n}}=O(n^{4\realpart{a}-1})\hbox{as $n\to\infty$.}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\Racah{n}@{\lambda(-a+ix)}{a+b-1}{c+d-1}{a+d-1}{a-d}{}=\frac{\Wilson{n}@{x^{2}}{a}{b}{c}{d}}{\pochhammer{a+b}{n}\pochhammer{a+c}{n}\pochhammer{a+d}{n}}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\Racah{n}@{x(x-N+\delta)}{\alpha}{\beta}{-N-1}{\delta}=\frac{\Wilson{n}@{-(x+\frac{1}{2}(\delta-N))^{2}}{\frac{1}{2}(\delta-N)}{\alpha+1-\frac{1}{2}(\delta-N)}{\beta+\frac{1}{2}(\delta+N)+1}{-\frac{1}{2}(\delta+N)}}{\pochhammer{\alpha+1}{n}\pochhammer{\beta+\delta+1}{n}\pochhammer{-N}{n}}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\lim_{d\rightarrow\infty}\frac{\Wilson{n}@{x^{2}}{a}{b}{c}{d}}{\pochhammer{a+d}{n}}=\ctsdualHahn{n}@{x^{2}}{a}{b}{c}}}}} Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {{{\lim_{t\rightarrow\infty}\frac{\Wilson{n}@{(x+t)^{2}}{a-it}{b-it}{c+it}{d+it}}{(-2t)^{n}n!}=\ctsHahn{n}@{x}{a}{b}{c}{d}}}}}