DLMF:35.7.E6 (Q9817)

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DLMF:35.7.E6
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    Statements

    Defining formula
    F 1 2 ⁡ ( a , b c ; 𝐓 ) = | 𝐈 - 𝐓 | c - a - b ⁢ F 1 2 ⁡ ( c - a , c - b c ; 𝐓 ) = | 𝐈 - 𝐓 | - a ⁢ F 1 2 ⁡ ( a , c - b c ; - 𝐓 ⁢ ( 𝐈 - 𝐓 ) - 1 ) = | 𝐈 - 𝐓 | - b ⁢ F 1 2 ⁡ ( c - a , b c ; - 𝐓 ⁢ ( 𝐈 - 𝐓 ) - 1 ) . Gauss-hypergeometric-of-matrix-pFq 2 1 𝑎 𝑏 𝑐 𝐓 superscript 𝐈 𝐓 𝑐 𝑎 𝑏 Gauss-hypergeometric-of-matrix-pFq 2 1 𝑐 𝑎 𝑐 𝑏 𝑐 𝐓 superscript 𝐈 𝐓 𝑎 Gauss-hypergeometric-of-matrix-pFq 2 1 𝑎 𝑐 𝑏 𝑐 𝐓 superscript 𝐈 𝐓 1 superscript 𝐈 𝐓 𝑏 Gauss-hypergeometric-of-matrix-pFq 2 1 𝑐 𝑎 𝑏 𝑐 𝐓 superscript 𝐈 𝐓 1 {\displaystyle{\displaystyle{{}_{2}F_{1}}\left({a,b\atop c};\mathbf{T}\right)=% |\mathbf{I}-\mathbf{T}|^{c-a-b}{{}_{2}F_{1}}\left({c-a,c-b\atop c};\mathbf{T}% \right)=|\mathbf{I}-\mathbf{T}|^{-a}{{}_{2}F_{1}}\left({a,c-b\atop c};-\mathbf% {T}(\mathbf{I}-\mathbf{T})^{-1}\right)=|\mathbf{I}-\mathbf{T}|^{-b}{{}_{2}F_{1% }}\left({c-a,b\atop c};-\mathbf{T}(\mathbf{I}-\mathbf{T})^{-1}\right).}}
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    DLMF id
    DLMF:35.7.E6
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