DLMF:29.10.E3 (Q8716)

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DLMF:29.10.E3
No description defined

    Statements

    Defining formula
    d 2 w d z ′ 2 + ( h ′ - ν ⁢ ( ν + 1 ) ⁢ k ′ 2 ⁢ sn 2 ⁡ ( z ′ , k ′ ) ) ⁢ w = 0 . derivative 𝑤 superscript 𝑧 ′ 2 superscript ℎ ′ 𝜈 𝜈 1 superscript superscript 𝑘 ′ 2 Jacobi-elliptic-sn 2 superscript 𝑧 ′ superscript 𝑘 ′ 𝑤 0 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z^{\prime}}^{2% }}+(h^{\prime}-\nu(\nu+1){k^{\prime}}^{2}{\operatorname{sn}^{2}}\left(z^{% \prime},k^{\prime}\right))w=0.}}
    0 references
    DLMF id
    DLMF:29.10.E3
    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.m2adec
    0 references
    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.m2adec
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    Q12348
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C29.S1.XMD6.m1adec
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    Q12349
    Defining formula
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C29.S1.XMD7.m1adec
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    Q12350
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C29.S1.XMD8.m1adec
    0 references
    Q12351
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C29.S1.XMD9.m1adec
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    Q12352
    Defining formula
    w ⁢ ( z ) 𝑤 𝑧 {\displaystyle{\displaystyle w(z)}}
    xml-id
    C29.S2.XMD1.m1dec
    0 references
     
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