DLMF:29.2.E2 (Q8575)

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DLMF:29.2.E2
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    Statements

    Defining formula
    d 2 w d ξ 2 + 1 2 ⁢ ( 1 ξ + 1 ξ - 1 + 1 ξ - k - 2 ) ⁢ d w d ξ + h ⁢ k - 2 - ν ⁢ ( ν + 1 ) ⁢ ξ 4 ⁢ ξ ⁢ ( ξ - 1 ) ⁢ ( ξ - k - 2 ) ⁢ w = 0 , derivative 𝑤 𝜉 2 1 2 1 𝜉 1 𝜉 1 1 𝜉 superscript 𝑘 2 derivative 𝑤 𝜉 ℎ superscript 𝑘 2 𝜈 𝜈 1 𝜉 4 𝜉 𝜉 1 𝜉 superscript 𝑘 2 𝑤 0 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}\xi}^{2}}+% \frac{1}{2}\left(\frac{1}{\xi}+\frac{1}{\xi-1}+\frac{1}{\xi-k^{-2}}\right)% \frac{\mathrm{d}w}{\mathrm{d}\xi}+\frac{hk^{-2}-\nu(\nu+1)\xi}{4\xi(\xi-1)(\xi% -k^{-2})}w=0,}}
    0 references
    DLMF id
    DLMF:29.2.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
    Q12349
    Defining formula
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C29.S1.XMD7.m1adec
    0 references
    Q12350
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C29.S1.XMD8.m1bdec
    0 references
    Q12351
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C29.S1.XMD9.m1adec
    0 references
    variable (locally)
    Defining formula
    ξ 𝜉 {\displaystyle{\displaystyle\xi}}
    xml-id
    C29.S2.XMD2.m1dec
    0 references
     
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