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

From DRMF
Jump to navigation Jump to search
← Older editNewer edit →
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1aadec

Revision as of 13:50, 2 January 2020

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

    Statements

    Defining formula
    ∫ 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
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q6307&oldid=40713"