Formula:KLS:09.02:14

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R n ⁡ ( λ ⁢ ( x ) ; α , β , γ , δ ) = ( n + α + β + 1 ) n ( α + 1 ) n ⁢ ( β + δ + 1 ) n ⁢ ( γ + 1 ) n ⁢ R ^ n ⁡ ( λ ⁢ ( x ) ) Racah-polynomial-R 𝑛 𝜆 𝑥 𝛼 𝛽 𝛾 𝛿 Pochhammer-symbol 𝑛 𝛼 𝛽 1 𝑛 Pochhammer-symbol 𝛼 1 𝑛 Pochhammer-symbol 𝛽 𝛿 1 𝑛 Pochhammer-symbol 𝛾 1 𝑛 Racah-polynomial-monic-p 𝑛 𝜆 𝑥 𝛼 𝛽 𝛾 𝛿 {\displaystyle{\displaystyle{\displaystyle R_{n}\!\left(\lambda(x);\alpha,% \beta,\gamma,\delta\right)=\frac{{\left(n+\alpha+\beta+1\right)_{n}}}{{\left(% \alpha+1\right)_{n}}{\left(\beta+\delta+1\right)_{n}}{\left(\gamma+1\right)_{n% }}}{\widehat{R}}_{n}\!\left(\lambda(x)\right)}}}

Substitution(s)

λ ⁢ ( x ) = x ⁢ ( x + γ + δ + 1 ) 𝜆 𝑥 𝑥 𝑥 𝛾 𝛿 1 {\displaystyle{\displaystyle{\displaystyle\lambda(x)=x(x+\gamma+\delta+1)}}}


Proof

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Symbols List

R n subscript 𝑅 𝑛 {\displaystyle{\displaystyle{\displaystyle R_{n}}}}  : Racah polynomial : http://dlmf.nist.gov/18.25#T1.t1.r4
( a ) n subscript 𝑎 𝑛 {\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}  : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii
R ^ n subscript ^ 𝑅 𝑛 {\displaystyle{\displaystyle{\displaystyle{\widehat{R}}_{n}}}}  : monic Racah polynomial : http://drmf.wmflabs.org/wiki/Definition:monicRacah

Bibliography

Equation in Section 9.2 of KLS.

URL links

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