DLMF:19.26.E13 (Q7263)

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DLMF:19.26.E13
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    Statements

    DLMF defining formula
    R C ⁡ ( α 2 , α 2 - θ ) + R C ⁡ ( β 2 , β 2 - θ ) = R C ⁡ ( σ 2 , σ 2 - θ ) , Carlson-integral-RC superscript 𝛼 2 superscript 𝛼 2 𝜃 Carlson-integral-RC superscript 𝛽 2 superscript 𝛽 2 𝜃 Carlson-integral-RC superscript 𝜎 2 superscript 𝜎 2 𝜃 {\displaystyle{\displaystyle R_{C}\left(\alpha^{2},\alpha^{2}-\theta\right)+R_% {C}\left(\beta^{2},\beta^{2}-\theta\right)=R_{C}\left(\sigma^{2},\sigma^{2}-% \theta\right),}}
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    constraint
    σ = ( α ⁢ β + θ ) / ( α + β ) 𝜎 𝛼 𝛽 𝜃 𝛼 𝛽 {\displaystyle{\displaystyle\sigma=(\alpha\beta+\theta)/(\alpha+\beta)}}
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    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.m2abdec
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    real or complex parameter
    DLMF defining formula
    α 2 superscript 𝛼 2 {\displaystyle{\displaystyle\alpha^{2}}}
    xml-id
    C19.S1.XMD7.m1dec
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    Identifiers

     
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