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DLMF:18.38.E2 - MaRDI portal

DLMF:18.38.E2 (Q6754)

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DLMF:18.38.E2
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    Statements

    DLMF defining formula
    ( d 2 / d x 2 ) ⁡ ln ⁡ V n ⁢ ( x ) = V n + 1 ⁢ ( x ) + V n - 1 ⁢ ( x ) - 2 ⁢ V n ⁢ ( x ) , derivative 𝑥 2 subscript 𝑉 𝑛 𝑥 subscript 𝑉 𝑛 1 𝑥 subscript 𝑉 𝑛 1 𝑥 2 subscript 𝑉 𝑛 𝑥 {\displaystyle{\displaystyle(\ifrac{{\mathrm{d}}^{2}}{{\mathrm{d}x}^{2}})\ln V% _{n}(x)=V_{n+1}(x)+V_{n-1}(x)-2V_{n}(x),}}
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    constraint
    n = 1 , 2 , … 𝑛 1 2 … {\displaystyle{\displaystyle n=1,2,\dots}}
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    Symbols used
    derivative of $$f$$ with respect to $$x$$
    DLMF 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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    principal branch of logarithm function
    DLMF defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
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    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1adec
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    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1adec
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    Identifiers

     
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