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=== Section 9.1 [[Wilson|Wilson]] ===
=== Section 9.1 [[Wilson|Wilson]] ===


==== [[Definition:normWilsonWtilde|normWilsonWtilde]]<ref>[[Formula:KLS:09.01:06]]</ref> ====
==== [[Definition:normWilsonWtilde|normWilsonWtilde]] ====
<math display=block>
<math display=block>
\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}}
\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}}
</math>
</math><ref>[[Formula:KLS:09.01:06]]</ref>  
==== [[Definition:monicWilson|monicWilson]]<ref>[[Formula:KLS:09.01:10]]</ref> ====
==== [[Definition:monicWilson|monicWilson]] ====
<math display=block>
<math display=block>
\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}.
\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}.
</math>
</math><ref>[[Formula:KLS:09.01:10]]</ref>


=== Section 9.2 [[Racah|Racah]] ===
=== Section 9.2 [[Racah|Racah]] ===
==== [[Definition:monicRacah|monicRacah]]<ref>[[Formula:KLS:09.02:14]]</ref> ====
==== [[Definition:monicRacah|monicRacah]] ====


<math display=block>
\Racah{n}@{\lambda(x)}{\alpha}{\beta}{\gamma}{\delta}=:
\frac{\pochhammer{n+\alpha+\beta+1}{n}}{\pochhammer{\alpha+1}{n}\pochhammer{\beta+\delta+1}{n}\pochhammer{\gamma+1}{n}}\monicRacah{n}@@{\lambda(x)}{\alpha}{\beta}{\gamma}{\delta}
</math><ref>[[Formula:KLS:09.02:14]]</ref>
=== Section 9.3 [[Continuous dual Hahn|Continuous dual Hahn]] ===
=== Section 9.3 [[Continuous dual Hahn|Continuous dual Hahn]] ===


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=== Section 9.5 [[Hahn|Hahn]] ===
=== Section 9.5 [[Hahn|Hahn]] ===
 
==== [[Definition:normctsHahnptilde|normctsHahnptilde]] ====
<ref>[[Formula:KLS:09.04:04]]</ref>
=== Section 9.6 [[Dual Hahn|Dual Hahn]] ===
=== Section 9.6 [[Dual Hahn|Dual Hahn]] ===



Revision as of 18:32, 13 July 2017

Symbols in KLS Chapter 9

Section 9.1 Wilson

normWilsonWtilde

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}} } [1]

monicWilson

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}. } [2]

Section 9.2 Racah

monicRacah

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Racah{n}@{\lambda(x)}{\alpha}{\beta}{\gamma}{\delta}=: \frac{\pochhammer{n+\alpha+\beta+1}{n}}{\pochhammer{\alpha+1}{n}\pochhammer{\beta+\delta+1}{n}\pochhammer{\gamma+1}{n}}\monicRacah{n}@@{\lambda(x)}{\alpha}{\beta}{\gamma}{\delta} } [3]

Section 9.3 Continuous dual Hahn

Section 9.4 Continuous Hahn

Section 9.5 Hahn

normctsHahnptilde

[4]

Section 9.6 Dual Hahn

Section 9.7 Meixner-Pollaczek

Section 9.8 Jacobi

Section 9.9Jacobi: Special cases

Section 9.10 Pseudo Jacobi

Section 9.11 Meixner

Section 9.12 Krawtchouk

Section 9.13 Laguerre

Section 9.14 Bessel

Section 9.15 Charlier

Section 9.16 Hermite