DLMF:19.10.E2 (Q6270): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: hyperbolic cosine function / rank
 
Normal rank
Property / Symbols used: hyperbolic cosine function / qualifier
 
Defining formula:

cosh z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}

\cosh@@{\NVar{z}}
Property / Symbols used: hyperbolic cosine function / qualifier
 
xml-id: C4.S28.E2.m2adec
Property / Symbols used
 
Property / Symbols used: hyperbolic sine function / rank
 
Normal rank
Property / Symbols used: hyperbolic sine function / qualifier
 
Defining formula:

sinh z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}

\sinh@@{\NVar{z}}
Property / Symbols used: hyperbolic sine function / qualifier
 
xml-id: C4.S28.E1.m2adec
Property / Symbols used
 
Property / Symbols used: Q11807 / rank
 
Normal rank
Property / Symbols used: Q11807 / qualifier
 
Defining formula:

ϕ italic-ϕ {\displaystyle{\displaystyle\phi}}

\phi
Property / Symbols used: Q11807 / qualifier
 
xml-id: C19.S1.XMD4.m1dec

Latest revision as of 13:47, 2 January 2020

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DLMF:19.10.E2
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    Statements

    ( sinh ϕ ) R C ( 1 , cosh 2 ϕ ) = gd ( ϕ ) . italic-ϕ Carlson-integral-RC 1 2 italic-ϕ Gudermannian italic-ϕ {\displaystyle{\displaystyle(\sinh\phi)R_{C}\left(1,{\cosh^{2}}\phi\right)=% \operatorname{gd}\left(\phi\right).}}
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    DLMF:19.10.E2
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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.m2aadec
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    gd x Gudermannian 𝑥 {\displaystyle{\displaystyle\operatorname{gd}\NVar{x}}}
    C4.S23.E39.m2adec
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    cosh z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    C4.S28.E2.m2adec
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    sinh z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    C4.S28.E1.m2adec
    0 references
    ϕ italic-ϕ {\displaystyle{\displaystyle\phi}}
    C19.S1.XMD4.m1dec
    0 references