DLMF:1.13.E17 (Q483)

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DLMF:1.13.E17
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    Statements

    Defining formula
    d 2 w d η 2 + g ⁢ ( z ) ⁢ exp ⁡ ( 2 ⁢ ∫ f ⁢ ( z ) ⁢ d z ) ⁢ w = 0 . derivative 𝑤 𝜂 2 𝑔 𝑧 2 𝑓 𝑧 𝑧 𝑤 0 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}\eta}^{2}}+g(z% )\exp\left(2\int f(z)\mathrm{d}z\right)w=0.}}
    0 references
    DLMF id
    DLMF:1.13.E17
    0 references
    Symbols used
    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.m2aedec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1addec
    0 references
    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2abdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3addec
    0 references
    Q10760
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C1.S1.XMD1.m1ndec
    0 references
    Q10858
    Defining formula
    w ⁢ ( z ) 𝑤 𝑧 {\displaystyle{\displaystyle w(z)}}
    xml-id
    C1.S13.XMD1.m1ddec
    0 references
    Q10859
    Defining formula
    f ⁢ ( z ) 𝑓 𝑧 {\displaystyle{\displaystyle f(z)}}
    xml-id
    C1.S13.XMD2.m1gdec
    0 references
    change of variable (locally)
    Defining formula
    η 𝜂 {\displaystyle{\displaystyle\eta}}
    xml-id
    C1.S13.XMD25.m1adec
    0 references
    Q10860
    Defining formula
    g ⁢ ( z ) 𝑔 𝑧 {\displaystyle{\displaystyle g(z)}}
    xml-id
    C1.S13.XMD3.m1ddec
    0 references
     
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