Definition:monicctsHahn: Difference between revisions

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Revision as of 00:32, 6 March 2017

The LaTeX DLMF and DRMF macro \monicctsHahn represents the monic continuous Hahn polynomial.

This macro is in the category of polynomials.

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

\monicctsHahn{n} produces p ^ n continuous-Hahn-polynomial-monic-p 𝑛 {\displaystyle{\displaystyle{\displaystyle{\widehat{p}}_{n}}}}
\monicctsHahn{n}@{x}{a}{b}{c}{d} produces p ^ n ( x ; a , b , c , d ) continuous-Hahn-polynomial-monic-p 𝑛 𝑥 𝑎 𝑏 𝑐 𝑑 {\displaystyle{\displaystyle{\displaystyle{\widehat{p}}_{n}\!\left(x;a,b,c,d% \right)}}}
\monicctsHahn{n}@@{x}{a}{b}{c}{d} produces p ^ n ( x ) continuous-Hahn-polynomial-monic-p 𝑛 𝑥 𝑎 𝑏 𝑐 𝑑 {\displaystyle{\displaystyle{\displaystyle{\widehat{p}}_{n}\!\left(x\right)}}}

These are defined by p n ( x ; a , b , c , d ) = : ( n + a + b + c + d - 1 ) n n ! p ^ n ( x ; a , b , c , d ) fragments continuous-Hahn-polynomial 𝑛 𝑥 𝑎 𝑏 𝑐 𝑑 : Pochhammer-symbol 𝑛 𝑎 𝑏 𝑐 𝑑 1 𝑛 𝑛 continuous-Hahn-polynomial-monic-p 𝑛 𝑥 𝑎 𝑏 𝑐 𝑑 {\displaystyle{\displaystyle{\displaystyle p_{n}\!\left(x;a,b,c,d\right)=:% \frac{{\left(n+a+b+c+d-1\right)_{n}}}{n!}{\widehat{p}}_{n}\!\left(x;a,b,c,d% \right)}}}

Symbols List

p ^ n subscript ^ 𝑝 𝑛 {\displaystyle{\displaystyle{\displaystyle{\widehat{p}}_{n}}}}  : monic continuous Hahn polynomial : http://drmf.wmflabs.org/wiki/Definition:monicctsHahn
p n subscript 𝑝 𝑛 {\displaystyle{\displaystyle{\displaystyle p_{n}}}}  : continuous Hahn polynomial : http://dlmf.nist.gov/18.19#P2.p1
( a ) n subscript 𝑎 𝑛 {\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}  : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii