DLMF:32.2.E9 (Q9163): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q12524 / rank
 
Normal rank
Property / Symbols used: Q12524 / qualifier
 
Defining formula:

α 𝛼 {\displaystyle{\displaystyle\alpha}}

\alpha
Property / Symbols used: Q12524 / qualifier
 
xml-id: C32.S2.XMD1.m1edec
Property / Symbols used
 
Property / Symbols used: Q12525 / rank
 
Normal rank
Property / Symbols used: Q12525 / qualifier
 
Defining formula:

β 𝛽 {\displaystyle{\displaystyle\beta}}

\beta
Property / Symbols used: Q12525 / qualifier
 
xml-id: C32.S2.XMD2.m1ddec
Property / Symbols used
 
Property / Symbols used: Q12526 / rank
 
Normal rank
Property / Symbols used: Q12526 / qualifier
 
Defining formula:

γ 𝛾 {\displaystyle{\displaystyle\gamma}}

\gamma
Property / Symbols used: Q12526 / qualifier
 
xml-id: C32.S2.XMD3.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12527 / rank
 
Normal rank
Property / Symbols used: Q12527 / qualifier
 
Defining formula:

δ 𝛿 {\displaystyle{\displaystyle\delta}}

\delta
Property / Symbols used: Q12527 / qualifier
 
xml-id: C32.S2.XMD4.m1cdec

Latest revision as of 13:48, 2 January 2020

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DLMF:32.2.E9
No description defined

    Statements

    d 2 u d ζ 2 = 1 u ( d u d ζ ) 2 - 1 ζ d u d ζ + u 2 ( α + γ u ) 4 ζ 2 + β 4 ζ + δ 4 u , derivative 𝑢 𝜁 2 1 𝑢 superscript derivative 𝑢 𝜁 2 1 𝜁 derivative 𝑢 𝜁 superscript 𝑢 2 𝛼 𝛾 𝑢 4 superscript 𝜁 2 𝛽 4 𝜁 𝛿 4 𝑢 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}u}{{\mathrm{d}\zeta}^{2}}=% \frac{1}{u}\left(\frac{\mathrm{d}u}{\mathrm{d}\zeta}\right)^{2}-\frac{1}{\zeta% }\frac{\mathrm{d}u}{\mathrm{d}\zeta}+\frac{u^{2}(\alpha+\gamma u)}{4\zeta^{2}}% +\frac{\beta}{4\zeta}+\frac{\delta}{4u},}}
    0 references
    DLMF:32.2.E9
    0 references
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    C1.S4.E4.m2agdec
    0 references
    α 𝛼 {\displaystyle{\displaystyle\alpha}}
    C32.S2.XMD1.m1edec
    0 references
    β 𝛽 {\displaystyle{\displaystyle\beta}}
    C32.S2.XMD2.m1ddec
    0 references
    γ 𝛾 {\displaystyle{\displaystyle\gamma}}
    C32.S2.XMD3.m1cdec
    0 references
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    C32.S2.XMD4.m1cdec
    0 references