DLMF:29.7.E5 (Q8700)

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DLMF:29.7.E5
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    Statements

    Defining formula
    b ν m + 1 ⁡ ( k 2 ) - a ν m ⁡ ( k 2 ) = O ⁡ ( ν m + 3 2 ⁢ ( 1 - k 1 + k ) ν ) , Lame-eigenvalue-b 𝑚 1 𝜈 superscript 𝑘 2 Lame-eigenvalue-a 𝑚 𝜈 superscript 𝑘 2 Big-O superscript 𝜈 𝑚 3 2 superscript 1 𝑘 1 𝑘 𝜈 {\displaystyle{\displaystyle b^{m+1}_{\nu}\left(k^{2}\right)-a^{m}_{\nu}\left(% k^{2}\right)=O\left(\nu^{m+\frac{3}{2}}\left(\frac{1-k}{1+k}\right)^{\nu}% \right),}}
    0 references
    DLMF id
    DLMF:29.7.E5
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    constraint
    ν → ∞ → 𝜈 {\displaystyle{\displaystyle\nu\to\infty}}
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    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2adec
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    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
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    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.m12adec
    0 references
    Q12357
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C29.S1.XMD1.m1bdec
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    Q12350
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C29.S1.XMD8.m1ddec
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    Q12351
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C29.S1.XMD9.m1bdec
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