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== Symbols in KLS Chapter 9 == | |||
== | |||
=== Section 9.1 [[Wilson|Wilson]] === | |||
==== [[Definition:normWilsonWtilde|normWilsonWtilde]] ==== | |||
<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}} | |||
</math><ref>[[Formula:KLS:09.01:06]]</ref> | |||
==== [[Definition:monicWilson|monicWilson]] ==== | |||
<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}. | |||
</math><ref>[[Formula:KLS:09.01:10]]</ref> | |||
=== Section 9.2 [[Racah|Racah]] === | |||
==== [[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 9.4 [[Continuous Hahn|Continuous Hahn]] === | |||
==== [[Definition:normctsHahnptilde|normctsHahnptilde]] ==== | |||
<math display=block> | |||
\normctsHahnptilde{n}@@{x}{a}{b}{c}{d}:=\normctsHahnptilde{n}@{x}{a}{b}{c}{d}=\frac{n!}{i^n\pochhammer{a+c}{n}\pochhammer{a+d}{n}}\ctsHahn{n}@{x}{a}{b}{c}{d}. | |||
</math><ref>[[Formula:KLS:09.04:04]]</ref> | |||
=== Section 9.5 [[Hahn|Hahn]] === | |||
=== Section 9.6 [[Dual Hahn|Dual Hahn]] === | |||
=== Section 9.7 [[Meixner-Pollaczek|Meixner-Pollaczek]] === | |||
=== Section 9.8 [[Jacobi|Jacobi]] === | |||
=== Section 9.9[[Jacobi: Special cases|Jacobi: Special cases]] === | |||
=== Section 9.10 [[Pseudo Jacobi|Pseudo Jacobi]] === | |||
=== Section 9.11 [[Meixner|Meixner]] === | |||
=== Section 9.12 [[Krawtchouk|Krawtchouk]] === | |||
=== Section 9.13 [[Laguerre|Laguerre]] === | |||
=== Section 9.14 [[Bessel|Bessel]] === | |||
=== Section 9.15 [[Charlier|Charlier]] === | |||
=== Section 9.16 [[Hermite|Hermite]] === | |||
== | |||
== | |||
Latest revision as of 18:43, 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
normctsHahnptilde
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \normctsHahnptilde{n}@@{x}{a}{b}{c}{d}:=\normctsHahnptilde{n}@{x}{a}{b}{c}{d}=\frac{n!}{i^n\pochhammer{a+c}{n}\pochhammer{a+d}{n}}\ctsHahn{n}@{x}{a}{b}{c}{d}. } [4]