DLMF:19.6.E8 (Q6158): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Legendre’s incomplete elliptic integral of the first kind / rank
 
Normal rank
Property / Symbols used: Legendre’s incomplete elliptic integral of the first kind / qualifier
 
Defining formula:

F ⁡ ( ϕ , k ) elliptic-integral-first-kind-F italic-ϕ 𝑘 {\displaystyle{\displaystyle F\left(\NVar{\phi},\NVar{k}\right)}}

\incellintFk@{\NVar{\phi}}{\NVar{k}}
Property / Symbols used: Legendre’s incomplete elliptic integral of the first kind / qualifier
 
xml-id: C19.S2.E4.m2aadec

Revision as of 13:40, 2 January 2020

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DLMF:19.6.E8
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    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
    Legendre’s incomplete elliptic integral of the first kind
    Defining formula
    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
     
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