DLMF:19.14.E2 (Q6307): Difference between revisions

From testwiki
Jump to navigation Jump to search
← Older editNewer edit →
imported>Admin
imported>Admin
Property / Symbols used
 
Property / Symbols used: Q11807 / rank
 
Normal rank
Property / Symbols used: Q11807 / qualifier
 
test:

ϕ italic-ϕ {\displaystyle{\displaystyle\phi}}

\phi
Property / Symbols used: Q11807 / qualifier
 
xml-id: C19.S1.XMD4.m1adec

Revision as of 12:50, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:19.14.E2
No description defined

    Statements

    test
    ∫ x 1 d t 1 - t 3 = 3 - 1 / 4 ⁢ F ⁡ ( ϕ , k ) , superscript subscript 𝑥 1 𝑡 1 superscript 𝑡 3 superscript 3 1 4 elliptic-integral-first-kind-F italic-ϕ 𝑘 {\displaystyle{\displaystyle\int_{x}^{1}\frac{\mathrm{d}t}{\sqrt{1-t^{3}}}=3^{% -1/4}F\left(\phi,k\right),}}
    0 references
    DLMF id
    DLMF:19.14.E2
    0 references
    constraint
    cos ⁡ ϕ = 3 - 1 + x 3 + 1 - x italic-ϕ 3 1 𝑥 3 1 𝑥 {\displaystyle{\displaystyle\cos\phi=\dfrac{\sqrt{3}-1+x}{\sqrt{3}+1-x}}}
    0 references
    cos ⁡ ϕ = 3 - 1 + x 3 + 1 - x italic-ϕ 3 1 𝑥 3 1 𝑥 {\displaystyle{\displaystyle\cos\phi=\dfrac{\sqrt{3}-1+x}{\sqrt{3}+1-x}}}
    0 references
    k 2 = 2 + 3 4 superscript 𝑘 2 2 3 4 {\displaystyle{\displaystyle k^{2}=\dfrac{2+\sqrt{3}}{4}}}
    0 references
    Symbols used
    cosine function
    test
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
    Legendre’s incomplete elliptic integral of the first kind
    test
    F ⁡ ( ϕ , k ) elliptic-integral-first-kind-F italic-ϕ 𝑘 {\displaystyle{\displaystyle F\left(\NVar{\phi},\NVar{k}\right)}}
    xml-id
    C19.S2.E4.m2aadec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aadec
    0 references
    Q11807
    test
    ϕ italic-ϕ {\displaystyle{\displaystyle\phi}}
    xml-id
    C19.S1.XMD4.m1adec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q6307&oldid=35884"