DLMF:32.2.E10 (Q9164)

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DLMF:32.2.E10
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    Statements

    Defining formula
    d 2 u d z 2 + 1 z ⁢ d u d z = 2 ⁢ α z ⁢ sin ⁡ u + 2 ⁢ γ ⁢ sin ⁡ ( 2 ⁢ u ) . derivative 𝑢 𝑧 2 1 𝑧 derivative 𝑢 𝑧 2 𝛼 𝑧 𝑢 2 𝛾 2 𝑢 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}u}{{\mathrm{d}z}^{2}}+\frac{% 1}{z}\frac{\mathrm{d}u}{\mathrm{d}z}=\frac{2\alpha}{z}\sin u+2\gamma\sin\left(% 2u\right).}}
    0 references
    DLMF id
    DLMF:32.2.E10
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    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.m2ahdec
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    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2adec
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    Q12523
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C32.S1.XMD4.m1hdec
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    Q12524
    Defining formula
    α 𝛼 {\displaystyle{\displaystyle\alpha}}
    xml-id
    C32.S2.XMD1.m1fdec
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