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DLMF:33.19.E7 - MaRDI portal

DLMF:33.19.E7 (Q10358)

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DLMF:33.19.E7
No description defined

    Statements

    DLMF defining formula
    β k - β k - 1 + 1 4 ⁢ ( k - 1 ) ⁢ ( k - 2 ⁢ ℓ - 2 ) ⁢ ϵ ⁢ β k - 2 + 1 2 ⁢ ( k - 1 ) ⁢ ϵ ⁢ γ k - 2 = 0 , subscript 𝛽 𝑘 subscript 𝛽 𝑘 1 1 4 𝑘 1 𝑘 2 ℓ 2 italic-ϵ subscript 𝛽 𝑘 2 1 2 𝑘 1 italic-ϵ subscript 𝛾 𝑘 2 0 {\displaystyle{\displaystyle\beta_{k}-\beta_{k-1}+\tfrac{1}{4}(k-1)(k-2\ell-2)% \epsilon\beta_{k-2}+\tfrac{1}{2}(k-1)\epsilon\gamma_{k-2}=0,}}
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    comment
    Warning: Falling back to standard tex;
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    constraint
    k = 2 , 3 , … 𝑘 2 3 … {\displaystyle{\displaystyle k=2,3,\dots}}
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    Symbols used
    nonnegative integer
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C33.S1.XMD1.m1fdec
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    nonnegative integer
    DLMF defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C33.S1.XMD2.m1fdec
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    real parameter
    DLMF defining formula
    ϵ italic-ϵ {\displaystyle{\displaystyle\epsilon}}
    xml-id
    C33.S1.XMD6.m1fdec
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    term
    DLMF defining formula
    γ k subscript 𝛾 𝑘 {\displaystyle{\displaystyle\gamma_{k}}}
    xml-id
    C33.S19.XMD2.m1bdec
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    term
    DLMF defining formula
    β k subscript 𝛽 𝑘 {\displaystyle{\displaystyle\beta_{k}}}
    xml-id
    C33.S19.XMD4.m1adec
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    Identifiers

     
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