DLMF:19.21.E1 (Q7115)

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DLMF:19.21.E1
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    Statements

    DLMF defining formula
    R F ⁡ ( 0 , z + 1 , z ) ⁢ R D ⁡ ( 0 , z + 1 , 1 ) + R D ⁡ ( 0 , z + 1 , z ) ⁢ R F ⁡ ( 0 , z + 1 , 1 ) = 3 ⁢ π / ( 2 ⁢ z ) , Carlson-integral-RF 0 𝑧 1 𝑧 Carlson-integral-RD 0 𝑧 1 1 Carlson-integral-RD 0 𝑧 1 𝑧 Carlson-integral-RF 0 𝑧 1 1 3 𝜋 2 𝑧 {\displaystyle{\displaystyle R_{F}\left(0,z+1,z\right)R_{D}\left(0,z+1,1\right% )+R_{D}\left(0,z+1,z\right)R_{F}\left(0,z+1,1\right)=3\pi/(2z),}}
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    constraint
    z ∈ ℂ ∖ ( - ∞ , 0 ] 𝑧 0 {\displaystyle{\displaystyle z\in\mathbb{C}\setminus(-\infty,0]}}
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    Symbols used
    elliptic integral symmetric in only two variables
    DLMF defining formula
    R D ⁡ ( x , y , z ) Carlson-integral-RD 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{D}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    xml-id
    C19.S16.E5.m2adec
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    symmetric elliptic integral of first kind
    DLMF 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.m2adec
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    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    Q10897
    DLMF defining formula
    ℂ {\displaystyle{\displaystyle\mathbb{C}}}
    xml-id
    introduction.Sx4.p1.t1.r1.m2adec
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    Q10758
    DLMF defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2adec
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    Q11215
    DLMF defining formula
    ( a , b ] 𝑎 𝑏 {\displaystyle{\displaystyle(\NVar{a},\NVar{b}]}}
    xml-id
    introduction.Sx4.p2.t1.r1.m3adec
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    Q10759
    DLMF defining formula
    ∖ {\displaystyle{\displaystyle\setminus}}
    xml-id
    introduction.Sx4.p2.t1.r19.m2adec
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    Identifiers

     
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