DLMF:29.5.E4 (Q8622)

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DLMF:29.5.E4
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    Statements

    Defining formula
    lim k → 1 - ⁡ a ν m ⁡ ( k 2 ) = lim k → 1 - ⁡ b ν m + 1 ⁡ ( k 2 ) = ν ⁢ ( ν + 1 ) - μ 2 , subscript → 𝑘 limit-from 1 Lame-eigenvalue-a 𝑚 𝜈 superscript 𝑘 2 subscript → 𝑘 limit-from 1 Lame-eigenvalue-b 𝑚 1 𝜈 superscript 𝑘 2 𝜈 𝜈 1 superscript 𝜇 2 {\displaystyle{\displaystyle\lim_{k\to 1-}a^{m}_{\nu}\left(k^{2}\right)=\lim_{% k\to 1-}b^{m+1}_{\nu}\left(k^{2}\right)=\nu(\nu+1)-\mu^{2},}}
    0 references
    DLMF id
    DLMF:29.5.E4
    0 references
    Symbols used
    Q12356
    Defining formula
    a ν n ⁡ ( k 2 ) Lame-eigenvalue-a 𝑛 𝜈 superscript 𝑘 2 {\displaystyle{\displaystyle a^{\NVar{n}}_{\NVar{\nu}}\left(\NVar{k^{2}}\right% )}}
    xml-id
    C29.S3.SS1.p1.m11aadec
    0 references
    Q12358
    Defining formula
    b ν n ⁡ ( k 2 ) Lame-eigenvalue-b 𝑛 𝜈 superscript 𝑘 2 {\displaystyle{\displaystyle b^{\NVar{n}}_{\NVar{\nu}}\left(\NVar{k^{2}}\right% )}}
    xml-id
    C29.S3.SS1.p1.m12aadec
    0 references
    Q12357
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C29.S1.XMD1.m1bdec
    0 references
    Q12350
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C29.S1.XMD8.m1dec
    0 references
    Q12351
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C29.S1.XMD9.m1cdec
    0 references
    Q12363
    Defining formula
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C29.S5.XMD1.m1dec
    0 references
     
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