Definition:ctsHahn

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

This macro is in the category of polynomials.

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

\ctsHahn{n} produces p n continuous-Hahn-polynomial 𝑛 {\displaystyle{\displaystyle{\displaystyle p_{n}}}}
\ctsHahn{n}@{x}{a}{b}{c}{d} produces p n ⁑ ( x ; a , b , c , d ) continuous-Hahn-polynomial 𝑛 π‘₯ π‘Ž 𝑏 𝑐 𝑑 {\displaystyle{\displaystyle{\displaystyle p_{n}\!\left(x;a,b,c,d\right)}}}
\ctsHahn{n}@@{x}{a}{b}{c}{d} produces p n ⁑ ( x ) continuous-Hahn-polynomial 𝑛 π‘₯ π‘Ž 𝑏 𝑐 𝑑 {\displaystyle{\displaystyle{\displaystyle p_{n}\!\left(x\right)}}}

These are defined by p n ⁑ ( x ; a , b , c , d ) := i n ⁒ ( a + c ) n ⁒ ( a + d ) n n ! ⁒ \HyperpFq ⁒ 32 ⁒ @ ⁒ @ - n , n + a + b + c + d - 1 , a + i ⁒ x ⁒ a + c , a + d ⁒ 1 assign continuous-Hahn-polynomial 𝑛 π‘₯ π‘Ž 𝑏 𝑐 𝑑 superscript 𝑖 𝑛 Pochhammer-symbol π‘Ž 𝑐 𝑛 Pochhammer-symbol π‘Ž 𝑑 𝑛 𝑛 \HyperpFq 32 @ @ 𝑛 𝑛 π‘Ž 𝑏 𝑐 𝑑 1 π‘Ž 𝑖 π‘₯ π‘Ž 𝑐 π‘Ž 𝑑 1 {\displaystyle{\displaystyle{\displaystyle p_{n}\!\left(x;a,b,c,d\right){}:=i^% {n}\frac{{\left(a+c\right)_{n}}{\left(a+d\right)_{n}}}{n!}\,\HyperpFq{3}{2}@@{% -n,n+a+b+c+d-1,a+ix}{a+c,a+d}{1}}}}

Symbols List

p n subscript 𝑝 𝑛 {\displaystyle{\displaystyle{\displaystyle p_{n}}}}  : continuous Hahn polynomial : http://dlmf.nist.gov/18.19#P2.p1
( a ) n subscript π‘Ž 𝑛 {\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}  : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii
F q p subscript subscript 𝐹 π‘ž 𝑝 {\displaystyle{\displaystyle{\displaystyle{{}_{p}F_{q}}}}}  : generalized hypergeometric function : http://dlmf.nist.gov/16.2#E1


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