Formula:KLS:09.02:19

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R n ( λ ( x + 1 ) ; α , β , γ , δ ) - R n ( λ ( x ) ; α , β , γ , δ ) = n ( n + α + β + 1 ) ( α + 1 ) ( β + δ + 1 ) ( γ + 1 ) ( 2 x + γ + δ + 2 ) R n - 1 ( λ ( x ) ; α + 1 , β + 1 , γ + 1 , δ ) Racah-polynomial-R 𝑛 𝜆 𝑥 1 𝛼 𝛽 𝛾 𝛿 Racah-polynomial-R 𝑛 𝜆 𝑥 𝛼 𝛽 𝛾 𝛿 𝑛 𝑛 𝛼 𝛽 1 𝛼 1 𝛽 𝛿 1 𝛾 1 2 𝑥 𝛾 𝛿 2 Racah-polynomial-R 𝑛 1 𝜆 𝑥 𝛼 1 𝛽 1 𝛾 1 𝛿 {\displaystyle{\displaystyle{\displaystyle R_{n}\!\left(\lambda(x+1);\alpha,% \beta,\gamma,\delta\right)-R_{n}\!\left(\lambda(x);\alpha,\beta,\gamma,\delta% \right){}=\frac{n(n+\alpha+\beta+1)}{(\alpha+1)(\beta+\delta+1)(\gamma+1)}{}(2% x+\gamma+\delta+2)R_{n-1}\!\left(\lambda(x);\alpha+1,\beta+1,\gamma+1,\delta% \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

Bibliography

Equation in Section 9.2 of KLS.

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