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=== Section 9.2 [[Racah|Racah]] ===
=== Section 9.2 [[Racah|Racah]] ===
==== [[Definition:monicRacah|monicRacah]]<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]] ===

Revision as of 19:28, 13 July 2017

Symbols in KLS Chapter 9

Section 9.1 Wilson

normWilsonWtilde[1]

W ~ n ⁡ ( x 2 ; a , b , c , d ) := W n ⁡ ( x 2 ; a , b , c , d ) ( a + b ) n ⁢ ( a + c ) n ⁢ ( a + d ) n assign Wilson-polynomial-normalized-W-tilde 𝑛 superscript 𝑥 2 𝑎 𝑏 𝑐 𝑑 Wilson-polynomial-W 𝑛 superscript 𝑥 2 𝑎 𝑏 𝑐 𝑑 Pochhammer-symbol 𝑎 𝑏 𝑛 Pochhammer-symbol 𝑎 𝑐 𝑛 Pochhammer-symbol 𝑎 𝑑 𝑛 {\displaystyle{\tilde{W}}_{n}\!\left(x^{2};a,b,c,d\right):=\frac{W_{n}\!\left(% x^{2};a,b,c,d\right)}{{\left(a+b\right)_{n}}{\left(a+c\right)_{n}}{\left(a+d% \right)_{n}}}}

monicWilson[2]

W n ⁡ ( x 2 ; a , b , c , d ) = : ( - 1 ) n ( n + a + b + c + d - 1 ) n W ^ n ⁡ ( x 2 ) . fragments Wilson-polynomial-W 𝑛 superscript 𝑥 2 𝑎 𝑏 𝑐 𝑑 : superscript fragments ( 1 ) 𝑛 Pochhammer-symbol 𝑛 𝑎 𝑏 𝑐 𝑑 1 𝑛 Wilson-polynomial-monic 𝑛 superscript 𝑥 2 𝑎 𝑏 𝑐 𝑑 . {\displaystyle W_{n}\!\left(x^{2};a,b,c,d\right)=:(-1)^{n}{\left(n+a+b+c+d-1% \right)_{n}}{\widehat{W}}_{n}\!\left(x^{2}\right).}

Section 9.2 Racah

monicRacah[3]

Section 9.3 Continuous dual Hahn

Section 9.4 Continuous Hahn

Section 9.5 Hahn

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

  1. ↑ Formula:KLS:09.01:06
  2. ↑ Formula:KLS:09.01:10
  3. ↑ Formula:KLS:09.02:14
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