DLMF:19.10.E2 (Q6966)

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DLMF:19.10.E2
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    Statements

    DLMF defining formula
    ( 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).}}
    0 references
    Symbols used
    Carlson’s combination of inverse circular and inverse hyperbolic functions
    DLMF 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.m2aadec
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    Gudermannian function
    DLMF defining formula
    gd ⁡ x Gudermannian 𝑥 {\displaystyle{\displaystyle\operatorname{gd}\NVar{x}}}
    xml-id
    C4.S23.E39.m2adec
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    hyperbolic cosine function
    DLMF defining formula
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2adec
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    hyperbolic sine function
    DLMF defining formula
    sinh ⁡ z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    xml-id
    C4.S28.E1.m2adec
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    real or complex argument
    DLMF defining formula
    ϕ italic-ϕ {\displaystyle{\displaystyle\phi}}
    xml-id
    C19.S1.XMD4.m1dec
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    Identifiers

     
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