DLMF:29.2.E4 (Q8577)

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DLMF:29.2.E4
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    Statements

    Defining formula
    ( 1 - k 2 ⁢ cos 2 ⁡ ϕ ) ⁢ d 2 w d ϕ 2 + k 2 ⁢ cos ⁡ ϕ ⁢ sin ⁡ ϕ ⁢ d w d ϕ + ( h - ν ⁢ ( ν + 1 ) ⁢ k 2 ⁢ cos 2 ⁡ ϕ ) ⁢ w = 0 , 1 superscript 𝑘 2 2 italic-ϕ derivative 𝑤 italic-ϕ 2 superscript 𝑘 2 italic-ϕ italic-ϕ derivative 𝑤 italic-ϕ ℎ 𝜈 𝜈 1 superscript 𝑘 2 2 italic-ϕ 𝑤 0 {\displaystyle{\displaystyle(1-k^{2}{\cos^{2}}\phi)\frac{{\mathrm{d}}^{2}w}{{% \mathrm{d}\phi}^{2}}+k^{2}\cos\phi\sin\phi\frac{\mathrm{d}w}{\mathrm{d}\phi}+(% h-\nu(\nu+1)k^{2}{\cos^{2}}\phi)w=0,}}
    0 references
    DLMF id
    DLMF:29.2.E4
    0 references
    Symbols used
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2adec
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    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.m2abdec
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    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2adec
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    Q12349
    Defining formula
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C29.S1.XMD7.m1bdec
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    Q12350
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C29.S1.XMD8.m1ddec
    0 references
    Q12351
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C29.S1.XMD9.m1bdec
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    change of variable (locally)
    Defining formula
    ϕ italic-ϕ {\displaystyle{\displaystyle\phi}}
    xml-id
    C29.S2.XMD3.m1dec
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