DLMF:19.36.E11 (Q6737)

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DLMF:19.36.E11
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    Statements

    Defining formula
    R F ⁑ ( 1 , 2 , 4 ) = R C ⁑ ( T 2 + M 2 , T 2 ) = 0.68508 58166 , Carlson-integral-RF 1 2 4 Carlson-integral-RC superscript 𝑇 2 superscript 𝑀 2 superscript 𝑇 2 0.68508 58166 {\displaystyle{\displaystyle R_{F}\left(1,2,4\right)=R_{C}\left(T^{2}+M^{2},T^% {2}\right)=0.68508\;58166,}}
    0 references
    DLMF id
    DLMF:19.36.E11
    0 references
    Symbols used
    Carlson’s combination of inverse circular and inverse hyperbolic functions
    Defining formula
    R C ⁑ ( x , y ) Carlson-integral-RC π‘₯ 𝑦 {\displaystyle{\displaystyle R_{C}\left(\NVar{x},\NVar{y}\right)}}
    xml-id
    C19.S2.E17.m2aadec
    0 references
    symmetric elliptic integral of first kind
    Defining formula
    R F ⁑ ( x , y , z ) Carlson-integral-RF π‘₯ 𝑦 𝑧 {\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    xml-id
    C19.S16.E1.m2addec
    0 references
    Q11942
    Defining formula
    M 𝑀 {\displaystyle{\displaystyle M}}
    xml-id
    C19.S36.XMD1.m1bdec
    0 references
    Q11943
    Defining formula
    T 𝑇 {\displaystyle{\displaystyle T}}
    xml-id
    C19.S36.XMD2.m1bdec
    0 references
     
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