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

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Property / Symbols used
 
Property / Symbols used: cosine function / rank
 
Normal rank
Property / Symbols used: cosine function / qualifier
 
test:

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

\cos@@{\NVar{z}}
Property / Symbols used: cosine function / qualifier
 
xml-id: C4.S14.E2.m2adec
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
 
test:

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
Property / Symbols used
 
Property / Symbols used: inverse Gudermannian function / rank
 
Normal rank
Property / Symbols used: inverse Gudermannian function / qualifier
 
test:

gd - 1 ( x ) inverse-Gudermannian 𝑥 {\displaystyle{\displaystyle{\operatorname{gd}^{-1}}\left(\NVar{x}\right)}}

\aGudermannian@{\NVar{x}}
Property / Symbols used: inverse Gudermannian function / qualifier
 
xml-id: C4.S23.E41.m2adec
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
test:

sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2adec
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

Latest revision as of 12:41, 2 January 2020

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DLMF:19.6.E8
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    Statements

    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
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    R C ( x , y ) Carlson-integral-RC 𝑥 𝑦 {\displaystyle{\displaystyle R_{C}\left(\NVar{x},\NVar{y}\right)}}
    C19.S2.E17.m2adec
    0 references
    cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    C4.S14.E2.m2adec
    0 references
    F ( ϕ , k ) elliptic-integral-first-kind-F italic-ϕ 𝑘 {\displaystyle{\displaystyle F\left(\NVar{\phi},\NVar{k}\right)}}
    C19.S2.E4.m2aadec
    0 references
    gd - 1 ( x ) inverse-Gudermannian 𝑥 {\displaystyle{\displaystyle{\operatorname{gd}^{-1}}\left(\NVar{x}\right)}}
    C4.S23.E41.m2adec
    0 references
    sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    C4.S14.E1.m2adec
    0 references
    ϕ italic-ϕ {\displaystyle{\displaystyle\phi}}
    C19.S1.XMD4.m1adec
    0 references