DLMF:29.18.E6 (Q8807)

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DLMF:29.18.E6
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    Statements

    Defining formula
    d 2 u 2 d β 2 + ( h - ν ⁢ ( ν + 1 ) ⁢ k 2 ⁢ sn 2 ⁡ ( β , k ) ) ⁢ u 2 = 0 , derivative subscript 𝑢 2 𝛽 2 ℎ 𝜈 𝜈 1 superscript 𝑘 2 Jacobi-elliptic-sn 2 𝛽 𝑘 subscript 𝑢 2 0 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}u_{2}}{{\mathrm{d}\beta}^{2}% }+(h-\nu(\nu+1)k^{2}{\operatorname{sn}^{2}}\left(\beta,k\right))u_{2}=0,}}
    0 references
    DLMF id
    DLMF:29.18.E6
    0 references
    Symbols used
    Jacobian elliptic function
    Defining formula
    sn ⁡ ( z , k ) Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E4.m2aadec
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    derivative of $$f$$ with respect to $$x$$
    Defining formula
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2aadec
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    Q12349
    Defining formula
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C29.S1.XMD7.m1dec
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    Q12350
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C29.S1.XMD8.m1bdec
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    Q12351
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C29.S1.XMD9.m1adec
    0 references
    Q12395
    Defining formula
    β 𝛽 {\displaystyle{\displaystyle\beta}}
    xml-id
    C29.S18.XMD4.m1cdec
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    Q12397
    Defining formula
    u j subscript 𝑢 𝑗 {\displaystyle{\displaystyle u_{j}}}
    xml-id
    C29.S18.XMD6.m1bdec
    0 references
     
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