DLMF:19.36.E9 (Q6733)

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DLMF:19.36.E9
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    Statements

    Defining formula
    R F ⁡ ( t 0 2 , t 0 2 + θ ⁢ c 0 2 , t 0 2 + θ ⁢ a 0 2 ) = R F ⁡ ( T 2 , T 2 , T 2 + θ ⁢ M 2 ) = R C ⁡ ( T 2 + θ ⁢ M 2 , T 2 ) . Carlson-integral-RF superscript subscript 𝑡 0 2 superscript subscript 𝑡 0 2 𝜃 superscript subscript 𝑐 0 2 superscript subscript 𝑡 0 2 𝜃 superscript subscript 𝑎 0 2 Carlson-integral-RF superscript 𝑇 2 superscript 𝑇 2 superscript 𝑇 2 𝜃 superscript 𝑀 2 Carlson-integral-RC superscript 𝑇 2 𝜃 superscript 𝑀 2 superscript 𝑇 2 {\displaystyle{\displaystyle R_{F}\left(t_{0}^{2},t_{0}^{2}+\theta c_{0}^{2},t% _{0}^{2}+\theta a_{0}^{2}\right)=R_{F}\left(T^{2},T^{2},T^{2}+\theta M^{2}% \right)=R_{C}\left(T^{2}+\theta M^{2},T^{2}\right).}}
    0 references
    DLMF id
    DLMF:19.36.E9
    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
    symmetric elliptic integral of first kind
    Defining formula
    R F ⁡ ( x , y , z ) Carlson-integral-RF 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    xml-id
    C19.S16.E1.m2acdec
    0 references
    Q11942
    Defining formula
    M 𝑀 {\displaystyle{\displaystyle M}}
    xml-id
    C19.S36.XMD1.m1dec
    0 references
    Q11943
    Defining formula
    T 𝑇 {\displaystyle{\displaystyle T}}
    xml-id
    C19.S36.XMD2.m1dec
    0 references
     
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