DLMF:29.3.E10 (Q8597)

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DLMF:29.3.E10
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    Statements

    Defining formula
    β p - H - α p - 1 ⁢ γ p β p - 1 - H - α p - 2 ⁢ γ p - 1 β p - 2 - H - ⁢ … = α p ⁢ γ p + 1 β p + 1 - H - α p + 1 ⁢ γ p + 2 β p + 2 - H - ⁢ ⋯ , subscript 𝛽 𝑝 𝐻 continued-fraction subscript 𝛼 𝑝 1 subscript 𝛾 𝑝 subscript 𝛽 𝑝 1 𝐻 continued-fraction subscript 𝛼 𝑝 2 subscript 𝛾 𝑝 1 subscript 𝛽 𝑝 2 limit-from 𝐻 … continued-fraction subscript 𝛼 𝑝 subscript 𝛾 𝑝 1 subscript 𝛽 𝑝 1 𝐻 continued-fraction subscript 𝛼 𝑝 1 subscript 𝛾 𝑝 2 subscript 𝛽 𝑝 2 limit-from 𝐻 ⋯ {\displaystyle{\displaystyle\beta_{p}-H-\cfrac{\alpha_{p-1}\gamma_{p}}{\beta_{% p-1}-H-\cfrac{\alpha_{p-2}\gamma_{p-1}}{\beta_{p-2}-H-}}\dots=\cfrac{\alpha_{p% }\gamma_{p+1}}{\beta_{p+1}-H-\cfrac{\alpha_{p+1}\gamma_{p+2}}{\beta_{p+2}-H-}}% \cdots,}}
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    DLMF id
    DLMF:29.3.E10
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    comment
    Warning: Falling back to standard tex;
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    Symbols used
    Q12359
    Defining formula
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C29.S1.XMD3.m1dec
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    DLMF:29.3.E9
    Defining formula
    H 𝐻 {\displaystyle{\displaystyle H}}
    xml-id
    C29.S3.XMD1.m1adec
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    DLMF:29.3.E11
    Defining formula
    α p subscript 𝛼 𝑝 {\displaystyle{\displaystyle\alpha_{p}}}
    xml-id
    C29.S3.XMD2.m1dec
    0 references
    Q12360
    Defining formula
    β p subscript 𝛽 𝑝 {\displaystyle{\displaystyle\beta_{p}}}
    xml-id
    C29.S3.XMD3.m1dec
    0 references
     
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