Definition:monicWilson: Difference between revisions

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Revision as of 00:33, 6 March 2017

The LaTeX DLMF and DRMF macro \monicWilson represents the monic Wilson polynomial.

This macro is in the category of polynomials.

In math mode, this macro can be called in the following ways:

\monicWilson{n} produces W ^ n Wilson-polynomial-monic 𝑛 {\displaystyle{\displaystyle{\displaystyle{\widehat{W}}_{n}}}}
\monicWilson{n}@{x^2}{a}{b}{c}{d} produces W ^ n ( x 2 ; a , b , c , d ) Wilson-polynomial-monic 𝑛 superscript 𝑥 2 𝑎 𝑏 𝑐 𝑑 {\displaystyle{\displaystyle{\displaystyle{\widehat{W}}_{n}\!\left(x^{2};a,b,c% ,d\right)}}}
\monicWilson{n}@@{x^2}{a}{b}{c}{d} produces W ^ n ( x 2 ) Wilson-polynomial-monic 𝑛 superscript 𝑥 2 𝑎 𝑏 𝑐 𝑑 {\displaystyle{\displaystyle{\displaystyle{\widehat{W}}_{n}\!\left(x^{2}\right% )}}}

These are defined by 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{\displaystyle{\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).}}}

Symbols List

W ^ n subscript ^ 𝑊 𝑛 {\displaystyle{\displaystyle{\displaystyle{\widehat{W}}_{n}}}}  : monic Wilson polynomial : http://drmf.wmflabs.org/wiki/Definition:monicWilson
W n subscript 𝑊 𝑛 {\displaystyle{\displaystyle{\displaystyle W_{n}}}}  : Wilson polynomial : http://dlmf.nist.gov/18.25#T1.t1.r2
( a ) n subscript 𝑎 𝑛 {\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}  : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii