Formula:KLS:09.02:24: Difference between revisions

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Latest revision as of 08:34, 22 December 2019


ω ⁢ ( x ; α , β , γ , δ ) ⁢ R n ⁡ ( λ ⁢ ( x ) ; α , β , γ , δ ) = ( γ + δ + 1 ) n ⁢ ( ∇ λ ) n ⁢ [ ω ⁢ ( x ; α + n , β + n , γ + n , δ ) ] 𝜔 𝑥 𝛼 𝛽 𝛾 𝛿 Racah-polynomial-R 𝑛 𝜆 𝑥 𝛼 𝛽 𝛾 𝛿 Pochhammer-symbol 𝛾 𝛿 1 𝑛 superscript subscript ∇ 𝜆 𝑛 delimited-[] 𝜔 𝑥 𝛼 𝑛 𝛽 𝑛 𝛾 𝑛 𝛿 {\displaystyle{\displaystyle{\displaystyle\omega(x;\alpha,\beta,\gamma,\delta)% R_{n}\!\left(\lambda(x);\alpha,\beta,\gamma,\delta\right){}={\left(\gamma+% \delta+1\right)_{n}}\left(\nabla_{\lambda}\right)^{n}\left[\omega(x;\alpha+n,% \beta+n,\gamma+n,\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
( a ) n subscript 𝑎 𝑛 {\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}  : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii

Bibliography

Equation in Section 9.2 of KLS.

URL links

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