DLMF:14.21.E1 (Q4946)

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DLMF:14.21.E1
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    Statements

    Defining formula
    ( 1 - z 2 ) ⁢ d 2 w d z 2 - 2 ⁢ z ⁢ d w d z + ( ν ⁢ ( ν + 1 ) - μ 2 1 - z 2 ) ⁢ w = 0 . 1 superscript 𝑧 2 derivative 𝑤 𝑧 2 2 𝑧 derivative 𝑤 𝑧 𝜈 𝜈 1 superscript 𝜇 2 1 superscript 𝑧 2 𝑤 0 {\displaystyle{\displaystyle\left(1-z^{2}\right)\frac{{\mathrm{d}}^{2}w}{{% \mathrm{d}z}^{2}}-2z\frac{\mathrm{d}w}{\mathrm{d}z}+\left(\nu(\nu+1)-\frac{\mu% ^{2}}{1-z^{2}}\right)w=0.}}
    0 references
    DLMF id
    DLMF:14.21.E1
    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.m2adec
    0 references
    Q11638
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C14.S1.XMD4.m1dec
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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.m1dec
    0 references
     
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