DLMF:10.21.E11 (Q3292): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: Q11427 / rank
 
Normal rank
Property / Symbols used: Q11427 / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11427 / qualifier
 
xml-id: C10.S1.XMD7.m1idec
Property / Symbols used
 
Property / Symbols used: Q11460 / rank
 
Normal rank
Property / Symbols used: Q11460 / qualifier
 
Defining formula:

ρ ν ( t ) subscript 𝜌 𝜈 𝑡 {\displaystyle{\displaystyle\rho_{\nu}(t)}}

\rho_{\nu}(t)
Property / Symbols used: Q11460 / qualifier
 
xml-id: C10.S21.XMD1.m1ddec

Latest revision as of 15:41, 2 January 2020

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DLMF:10.21.E11
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    Statements

    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
    DLMF:10.21.E11
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aadec
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    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    C1.S4.E4.m2aadec
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    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    C10.S1.XMD7.m1idec
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    ρ ν ( t ) subscript 𝜌 𝜈 𝑡 {\displaystyle{\displaystyle\rho_{\nu}(t)}}
    C10.S21.XMD1.m1ddec
    0 references