Definition:dualHahn: Difference between revisions

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Latest revision as of 08:50, 22 December 2019

The LaTeX DLMF and DRMF macro \dualHahn represents the Dual Hahn polynomial.

This macro is in the category of polynomials.

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

\dualHahn{n} produces R n dual-Hahn-R 𝑛 {\displaystyle{\displaystyle{\displaystyle R_{n}}}}
\dualHahn{n}@{\lambda(x)}{\gamma}{\delta}{N} produces R n ( λ ( x ) ; γ , δ , N ) dual-Hahn-R 𝑛 𝜆 𝑥 𝛾 𝛿 𝑁 {\displaystyle{\displaystyle{\displaystyle R_{n}\!\left(\lambda(x);\gamma,% \delta,N\right)}}}
\dualHahn{n}@@{\lambda(x)}{\gamma}{\delta}{N} produces R n ( λ ( x ) ) dual-Hahn-R 𝑛 𝜆 𝑥 𝛾 𝛿 𝑁 {\displaystyle{\displaystyle{\displaystyle R_{n}\!\left(\lambda(x)\right)}}}

These are defined by R n ( λ ( x ) ; γ , δ , N ) := \HyperpFq 32 @ @ - n , - x , x + γ + δ + 1 γ + 1 , - N 1 assign dual-Hahn-R 𝑛 𝜆 𝑥 𝛾 𝛿 𝑁 \HyperpFq 32 @ @ 𝑛 𝑥 𝑥 𝛾 𝛿 1 𝛾 1 𝑁 1 {\displaystyle{\displaystyle{\displaystyle R_{n}\!\left(\lambda(x);\gamma,% \delta,N\right):=\HyperpFq{3}{2}@@{-n,-x,x+\gamma+\delta+1}{\gamma+1,-N}{1}}}}

Symbols List

R n subscript 𝑅 𝑛 {\displaystyle{\displaystyle{\displaystyle R_{n}}}}  : dual Hahn polynomial : http://dlmf.nist.gov/18.25#T1.t1.r5
F q p subscript subscript 𝐹 𝑞 𝑝 {\displaystyle{\displaystyle{\displaystyle{{}_{p}F_{q}}}}}  : generalized hypergeometric function : http://dlmf.nist.gov/16.2#E1