DLMF:19.14.E3 (Q6308): 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: cosine function / rank
 
Normal rank
Property / Symbols used: cosine function / qualifier
 
Defining formula:

cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}

\cos@@{\NVar{z}}
Property / Symbols used: cosine function / qualifier
 
xml-id: C4.S14.E2.m2abdec

Revision as of 13:50, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:19.14.E3
No description defined

    Statements

    Defining formula
    ∫ 0 x d t 1 + t 4 = sign ⁡ ( x ) 2 ⁢ F ⁡ ( ϕ , k ) , superscript subscript 0 𝑥 𝑡 1 superscript 𝑡 4 sign 𝑥 2 elliptic-integral-first-kind-F italic-ϕ 𝑘 {\displaystyle{\displaystyle\int_{0}^{x}\frac{\mathrm{d}t}{\sqrt{1+t^{4}}}=% \frac{\operatorname{sign}\left(x\right)}{2}F\left(\phi,k\right),}}
    0 references
    DLMF id
    DLMF:19.14.E3
    0 references
    constraint
    cos ⁡ ϕ = 1 - x 2 1 + x 2 italic-ϕ 1 superscript 𝑥 2 1 superscript 𝑥 2 {\displaystyle{\displaystyle\cos\phi=\dfrac{1-x^{2}}{1+x^{2}}}}
    0 references
    cos ⁡ ϕ = 1 - x 2 1 + x 2 italic-ϕ 1 superscript 𝑥 2 1 superscript 𝑥 2 {\displaystyle{\displaystyle\cos\phi=\dfrac{1-x^{2}}{1+x^{2}}}}
    0 references
    k 2 = 1 2 superscript 𝑘 2 1 2 {\displaystyle{\displaystyle k^{2}=\dfrac{1}{2}}}
    0 references
    Symbols used
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2abdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q6308&oldid=40740"