Definition:ctsdualHahn

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Definition:ctsHahn >>

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

This macro is in the category of polynomials.

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

\ctsdualHahn{n} produces ${\displaystyle{\displaystyle{\displaystyle S_{n}}}}$

\ctsdualHahn{n}@{x^2}{a}{b}{c} produces ${\displaystyle{\displaystyle{\displaystyle S_{n}\!\left(x^{2};a,b,c\right)}}}$

\ctsdualHahn{n}@@{x^2}{a}{b}{c} produces ${\displaystyle{\displaystyle{\displaystyle S_{n}\!\left(x^{2}\right)}}}$

These are defined by ${\displaystyle{\displaystyle{\displaystyle\frac{S_{n}\!\left(x^{2};a,b,c\right)}{{\left(a+b\right)_{n}}{\left(a+c\right)_{n}}}:=\HyperpFq{3}{2}@@{-n,a+ix,a-ix}{a+b,a+c}{1}}}}$

Symbols List

${\displaystyle{\displaystyle{\displaystyle S_{n}}}}$ : continuous dual Hahn polynomial : http://dlmf.nist.gov/18.25#T1.t1.r3
${\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}$ : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii
${\displaystyle{\displaystyle{\displaystyle{{}_{p}F_{q}}}}}$ : generalized hypergeometric function : http://dlmf.nist.gov/16.2#E1

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