DLMF:14.2.E2 (Q4680)

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DLMF:14.2.E2
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    Statements

    Defining formula
    ( 1 - x 2 ) ⁢ d 2 w d x 2 - 2 ⁢ x ⁢ d w d x + ( ν ⁢ ( ν + 1 ) - μ 2 1 - x 2 ) ⁢ w = 0 . 1 superscript 𝑥 2 derivative 𝑤 𝑥 2 2 𝑥 derivative 𝑤 𝑥 𝜈 𝜈 1 superscript 𝜇 2 1 superscript 𝑥 2 𝑤 0 {\displaystyle{\displaystyle\left(1-x^{2}\right)\frac{{\mathrm{d}}^{2}w}{{% \mathrm{d}x}^{2}}-2x\frac{\mathrm{d}w}{\mathrm{d}x}+\left(\nu(\nu+1)-\frac{\mu% ^{2}}{1-x^{2}}\right)w=0.}}
    0 references
    DLMF id
    DLMF:14.2.E2
    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.m2aadec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1adec
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    Q11591
    Defining formula
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C14.S1.XMD7.m1dec
    0 references
    Q11590
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C14.S1.XMD8.m1adec
    0 references
     
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