DLMF:8.12.E10 (Q2606)

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DLMF:8.12.E10
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    Statements

    Defining formula
    c k ⁢ ( η ) = 1 η ⁢ d d η ⁡ c k - 1 ⁢ ( η ) + ( - 1 ) k ⁢ g k μ , subscript 𝑐 𝑘 𝜂 1 𝜂 derivative 𝜂 subscript 𝑐 𝑘 1 𝜂 superscript 1 𝑘 subscript 𝑔 𝑘 𝜇 {\displaystyle{\displaystyle c_{k}(\eta)=\frac{1}{\eta}\frac{\mathrm{d}}{% \mathrm{d}\eta}c_{k-1}(\eta)+(-1)^{k}\frac{g_{k}}{\mu},}}
    0 references
    DLMF id
    DLMF:8.12.E10
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    constraint
    k = 1 , 2 , … 𝑘 1 2 … {\displaystyle{\displaystyle k=1,2,\dots}}
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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.m2aadec
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    Q11330
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C8.S1.XMD5.m1bdec
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    Q11348
    Defining formula
    η ⁢ ( λ ) 𝜂 𝜆 {\displaystyle{\displaystyle\eta(\lambda)}}
    xml-id
    C8.S12.XMD1.m1idec
    0 references
    Q11352
    Defining formula
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C8.S12.XMD5.m1adec
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    Q11351
    Defining formula
    c k ⁢ ( η ) subscript 𝑐 𝑘 𝜂 {\displaystyle{\displaystyle c_{k}(\eta)}}
    xml-id
    C8.S12.XMD6.m1cdec
    0 references
    Q11353
    Defining formula
    g k subscript 𝑔 𝑘 {\displaystyle{\displaystyle g_{k}}}
    xml-id
    C8.S12.XMD7.m1dec
    0 references
     
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