DLMF:19.6.E8 (Q6158)

From DRMF
Revision as of 13:40, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:19.6.E8
No description defined

    Statements

    Defining formula
    F ⁡ ( ϕ , 1 ) = ( sin ⁡ ϕ ) ⁢ R C ⁡ ( 1 , cos 2 ⁡ ϕ ) = gd - 1 ⁡ ( ϕ ) . elliptic-integral-first-kind-F italic-ϕ 1 italic-ϕ Carlson-integral-RC 1 2 italic-ϕ inverse-Gudermannian italic-ϕ {\displaystyle{\displaystyle F\left(\phi,1\right)=(\sin\phi)R_{C}\left(1,{\cos% ^{2}}\phi\right)={\operatorname{gd}^{-1}}\left(\phi\right).}}
    0 references
    DLMF id
    DLMF:19.6.E8
    0 references
    Symbols used
    Carlson’s combination of inverse circular and inverse hyperbolic functions
    Defining formula
    R C ⁡ ( x , y ) Carlson-integral-RC 𝑥 𝑦 {\displaystyle{\displaystyle R_{C}\left(\NVar{x},\NVar{y}\right)}}
    xml-id
    C19.S2.E17.m2adec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2adec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q6158&oldid=38937"