Definition:monicHahn

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

This macro is in the category of polynomials.

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

\monicHahn{n} produces Q ^ n Hahn-polynomial-monic-p 𝑛 {\displaystyle{\displaystyle{\displaystyle{\widehat{Q}}_{n}}}}
\monicHahn{n}@{x}{\alpha}{\beta}{N} produces Q ^ n ⁑ ( x ; Ξ± , Ξ² , N ) Hahn-polynomial-monic-p 𝑛 π‘₯ 𝛼 𝛽 𝑁 {\displaystyle{\displaystyle{\displaystyle{\widehat{Q}}_{n}\!\left(x;\alpha,% \beta,N\right)}}}
\monicHahn{n}@@{x}{\alpha}{\beta}{N} produces Q ^ n ⁑ ( x ) Hahn-polynomial-monic-p 𝑛 π‘₯ 𝛼 𝛽 𝑁 {\displaystyle{\displaystyle{\displaystyle{\widehat{Q}}_{n}\!\left(x\right)}}}

These are defined by Q n ⁑ ( x ; Ξ± , Ξ² , N ) = : ( n + Ξ± + Ξ² + 1 ) n ( Ξ± + 1 ) n ⁒ ( - N ) n Q ^ n ⁑ ( x ; Ξ± , Ξ² , N ) fragments Hahn-polynomial-Q 𝑛 π‘₯ 𝛼 𝛽 𝑁 : Pochhammer-symbol 𝑛 𝛼 𝛽 1 𝑛 Pochhammer-symbol 𝛼 1 𝑛 Pochhammer-symbol 𝑁 𝑛 Hahn-polynomial-monic-p 𝑛 π‘₯ 𝛼 𝛽 𝑁 {\displaystyle{\displaystyle{\displaystyle Q_{n}\!\left(x;\alpha,\beta,N\right% )=:\frac{{\left(n+\alpha+\beta+1\right)_{n}}}{{\left(\alpha+1\right)_{n}}{% \left(-N\right)_{n}}}{\widehat{Q}}_{n}\!\left(x;\alpha,\beta,N\right)}}}

Symbols List

Q ^ n subscript ^ 𝑄 𝑛 {\displaystyle{\displaystyle{\displaystyle{\widehat{Q}}_{n}}}}  : monic Hahn polynomial : http://drmf.wmflabs.org/wiki/Definition:monicHahn
Q n subscript 𝑄 𝑛 {\displaystyle{\displaystyle{\displaystyle Q_{n}}}}  : Hahn polynomial : http://dlmf.nist.gov/18.19#T1.t1.r3
( a ) n subscript π‘Ž 𝑛 {\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}  : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii


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