DLMF:18.26.E15 (Q5945)

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DLMF:18.26.E15
No description defined

    Statements

    Defining formula
    δ y ( S n ⁡ ( y 2 ; a , b , c ) ) / δ y ( y 2 ) = - n ⁢ S n - 1 ⁡ ( y 2 ; a + 1 2 , b + 1 2 , c + 1 2 ) . central-difference 𝑦 continuous-dual-Hahn-S 𝑛 superscript 𝑦 2 𝑎 𝑏 𝑐 central-difference 𝑦 superscript 𝑦 2 𝑛 continuous-dual-Hahn-S 𝑛 1 superscript 𝑦 2 𝑎 1 2 𝑏 1 2 𝑐 1 2 {\displaystyle{\displaystyle\ifrac{\delta_{y}\left(S_{n}\left(y^{2};a,b,c% \right)\right)}{\delta_{y}(y^{2})}=-nS_{n-1}\left(y^{2};a+\tfrac{1}{2},b+% \tfrac{1}{2},c+\tfrac{1}{2}\right).}}
    0 references
    DLMF id
    DLMF:18.26.E15
    0 references
    Symbols used
    Q11767
    Defining formula
    δ x central-difference 𝑥 {\displaystyle{\displaystyle\delta_{\NVar{x}}}}
    xml-id
    C18.S1.EGx3.m1aadec
    0 references
    Q11784
    Defining formula
    S n ⁡ ( x ; a , b , c ) continuous-dual-Hahn-S 𝑛 𝑥 𝑎 𝑏 𝑐 {\displaystyle{\displaystyle S_{\NVar{n}}\left(\NVar{x};\NVar{a},\NVar{b},% \NVar{c}\right)}}
    xml-id
    C18.S25.T1.t1.r3.m2acdec
    0 references
    Q11743
    Defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C18.S1.XMD1.m1edec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1mdec
    0 references
     
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