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DLMF:18.26.E16 - MaRDI portal

DLMF:18.26.E16 (Q6642)

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DLMF:18.26.E16
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    Statements

    DLMF defining formula
    Δ y ( R n ⁡ ( y ⁢ ( y + γ + δ + 1 ) ; α , β , γ , δ ) ) Δ y ( y ⁢ ( y + γ + δ + 1 ) ) = n ⁢ ( n + α + β + 1 ) ( α + 1 ) ⁢ ( β + δ + 1 ) ⁢ ( γ + 1 ) ⁢ R n - 1 ⁡ ( y ⁢ ( y + γ + δ + 2 ) ; α + 1 , β + 1 , γ + 1 , δ ) . forward-difference 𝑦 Racah-polynomial-R 𝑛 𝑦 𝑦 𝛾 𝛿 1 𝛼 𝛽 𝛾 𝛿 forward-difference 𝑦 𝑦 𝑦 𝛾 𝛿 1 𝑛 𝑛 𝛼 𝛽 1 𝛼 1 𝛽 𝛿 1 𝛾 1 Racah-polynomial-R 𝑛 1 𝑦 𝑦 𝛾 𝛿 2 𝛼 1 𝛽 1 𝛾 1 𝛿 {\displaystyle{\displaystyle\frac{\Delta_{y}\left(R_{n}\left(y(y+\gamma+\delta% +1);\alpha,\beta,\gamma,\delta\right)\right)}{\Delta_{y}\left(y(y+\gamma+% \delta+1)\right)}=\frac{n(n+\alpha+\beta+1)}{(\alpha+1)(\beta+\delta+1)(\gamma% +1)}\*R_{n-1}\left(y(y+\gamma+\delta+2);\alpha+1,\beta+1,\gamma+1,\delta\right% ).}}
    0 references
    Symbols used
    Racah polynomial
    DLMF defining formula
    R n ⁡ ( x ; α , β , γ , ) Racah-polynomial-R 𝑛 𝑥 𝛼 𝛽 𝛾 {\displaystyle{\displaystyle R_{\NVar{n}}\left(\NVar{x};\NVar{\alpha},\NVar{% \beta},\NVar{\gamma},\right)\)\@add@PDF@RDFa@triples\end{document}}}
    xml-id
    C18.S25.T1.t1.r4.m2acdec
    0 references
    Q11071
    DLMF defining formula
    Δ forward-difference {\displaystyle{\displaystyle\Delta}}
    xml-id
    C3.S6.SS1.p1.m2adec
    0 references
    real variable
    DLMF defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C18.S1.XMD1.m1fdec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1ndec
    0 references
    arbitary small positive constant
    DLMF defining formula
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C18.S1.XMD8.m1ddec
    0 references

    Identifiers

     
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