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DLMF:10.21.E11 - MaRDI portal

DLMF:10.21.E11 (Q3989)

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DLMF:10.21.E11
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    Statements

    DLMF defining formula
    2 ⁢ ρ ν 2 ⁢ d ρ ν d t ⁢ d 3 ρ ν d t 3 - 3 ⁢ ρ ν 2 ⁢ ( d 2 ρ ν d t 2 ) 2 - 4 ⁢ π 2 ⁢ ρ ν 2 ⁢ ( d ρ ν d t ) 2 + ( 4 ⁢ ρ ν 2 + 1 - 4 ⁢ ν 2 ) ⁢ ( d ρ ν d t ) 4 = 0 . 2 superscript subscript 𝜌 𝜈 2 derivative subscript 𝜌 𝜈 𝑡 derivative subscript 𝜌 𝜈 𝑡 3 3 superscript subscript 𝜌 𝜈 2 superscript derivative subscript 𝜌 𝜈 𝑡 2 2 4 superscript 𝜋 2 superscript subscript 𝜌 𝜈 2 superscript derivative subscript 𝜌 𝜈 𝑡 2 4 superscript subscript 𝜌 𝜈 2 1 4 superscript 𝜈 2 superscript derivative subscript 𝜌 𝜈 𝑡 4 0 {\displaystyle{\displaystyle 2\rho_{\nu}^{2}\frac{\mathrm{d}\rho_{\nu}}{% \mathrm{d}t}\frac{{\mathrm{d}}^{3}\rho_{\nu}}{{\mathrm{d}t}^{3}}-3\rho_{\nu}^{% 2}\*\left(\frac{{\mathrm{d}}^{2}\rho_{\nu}}{{\mathrm{d}t}^{2}}\right)^{2}-4\pi% ^{2}\rho_{\nu}^{2}\*\left(\frac{\mathrm{d}\rho_{\nu}}{\mathrm{d}t}\right)^{2}+% (4\rho_{\nu}^{2}+1-4\nu^{2})\left(\frac{\mathrm{d}\rho_{\nu}}{\mathrm{d}t}% \right)^{4}=0.}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    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.m2aadec
    0 references
    complex parameter
    DLMF defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1idec
    0 references
    zero of cylinder function
    DLMF defining formula
    ρ ν ⁢ ( t ) subscript 𝜌 𝜈 𝑡 {\displaystyle{\displaystyle\rho_{\nu}(t)}}
    xml-id
    C10.S21.XMD1.m1ddec
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    Identifiers

     
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