DLMF:16.16.E5 (Q5271)

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DLMF:16.16.E5
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    Statements

    Defining formula
    F 3 ⁡ ( α , γ - α ; β , γ - β ; γ ; x , y ) = ( 1 - y ) α + β - γ ⁢ F 1 2 ⁡ ( α , β γ ; x + y - x ⁢ y ) , Appell-F-3 𝛼 𝛾 𝛼 𝛽 𝛾 𝛽 𝛾 𝑥 𝑦 superscript 1 𝑦 𝛼 𝛽 𝛾 Gauss-hypergeometric-F-as-2F1 𝛼 𝛽 𝛾 𝑥 𝑦 𝑥 𝑦 {\displaystyle{\displaystyle{F_{3}}\left(\alpha,\gamma-\alpha;\beta,\gamma-% \beta;\gamma;x,y\right)=(1-y)^{\alpha+\beta-\gamma}{{}_{2}F_{1}}\left({\alpha,% \beta\atop\gamma};x+y-xy\right),}}
    0 references
    DLMF id
    DLMF:16.16.E5
    0 references
    Symbols used
    third Appell function
    Defining formula
    Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "XMLReader::XML(): Argument #1 ($source) cannot be empty"): {\displaystyle \AppellF{3}@{\NVar{\alpha}}{\NVar{\alpha^{\prime}}}{\NVar{\beta}}{\NVar{\beta^% {\prime}}}{\NVar{\gamma}}{\NVar{x}}{\NVar{y}}}
    xml-id
    C16.S13.E3.m2aadec
    0 references
     
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