DLMF:9.10.E10 (Q2892)

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DLMF:9.10.E10
No description defined

    Statements

    Defining formula
    ∫ z n + 3 ⁢ w ⁢ ( z ) ⁢ d z = z n + 2 ⁢ w ′ ⁢ ( z ) - ( n + 2 ) ⁢ z n + 1 ⁢ w ⁢ ( z ) + ( n + 1 ) ⁢ ( n + 2 ) ⁢ ∫ z n ⁢ w ⁢ ( z ) ⁢ d z , superscript 𝑧 𝑛 3 𝑤 𝑧 𝑧 superscript 𝑧 𝑛 2 superscript 𝑤 ′ 𝑧 𝑛 2 superscript 𝑧 𝑛 1 𝑤 𝑧 𝑛 1 𝑛 2 superscript 𝑧 𝑛 𝑤 𝑧 𝑧 {\displaystyle{\displaystyle\int z^{n+3}w(z)\mathrm{d}z=z^{n+2}w^{\prime}(z)-(% n+2)z^{n+1}w(z)+(n+1)(n+2)\int z^{n}w(z)\mathrm{d}z,}}
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    DLMF id
    DLMF:9.10.E10
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    constraint
    n = 0 , 1 , 2 , … . 𝑛 0 1 2 … {\displaystyle{\displaystyle n=0,1,2,\ldots.}}
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    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aidec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aidec
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    Q11381
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1edec
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    ODE solution (locally)
    Defining formula
    w 𝑤 {\displaystyle{\displaystyle w}}
    xml-id
    C9.S2.XMD1.m1bdec
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