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DLMF:18.33.E6 - MaRDI portal

DLMF:18.33.E6 (Q6708)

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DLMF:18.33.E6
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    Statements

    DLMF defining formula
    κ n ⁢ ϕ n ⁢ ( 0 ) ⁢ ϕ n + 1 ⁢ ( z ) + κ n - 1 ⁢ ϕ n + 1 ⁢ ( 0 ) ⁢ z ⁢ ϕ n - 1 ⁢ ( z ) = ( κ n ⁢ ϕ n + 1 ⁢ ( 0 ) + κ n + 1 ⁢ ϕ n ⁢ ( 0 ) ⁢ z ) ⁢ ϕ n ⁢ ( z ) . subscript 𝜅 𝑛 subscript italic-ϕ 𝑛 0 subscript italic-ϕ 𝑛 1 𝑧 subscript 𝜅 𝑛 1 subscript italic-ϕ 𝑛 1 0 𝑧 subscript italic-ϕ 𝑛 1 𝑧 subscript 𝜅 𝑛 subscript italic-ϕ 𝑛 1 0 subscript 𝜅 𝑛 1 subscript italic-ϕ 𝑛 0 𝑧 subscript italic-ϕ 𝑛 𝑧 {\displaystyle{\displaystyle\kappa_{n}\phi_{n}(0)\phi_{n+1}(z)+\kappa_{n-1}% \phi_{n+1}(0)z\phi_{n-1}(z)=\left(\kappa_{n}\phi_{n+1}(0)+\kappa_{n+1}\phi_{n}% (0)z\right)\phi_{n}(z).}}
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    comment
    Warning: Falling back to standard tex;
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    Symbols used
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C18.S1.XMD2.m1edec
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    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1edec
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    polynomials
    DLMF defining formula
    ϕ n ⁢ ( z ) subscript italic-ϕ 𝑛 𝑧 {\displaystyle{\displaystyle\phi_{n}(z)}}
    xml-id
    C18.S33.XMD1.m1edec
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    Identifiers

     
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