DLMF:15.8.E7 (Q5064)

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DLMF:15.8.E7
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    Statements

    Defining formula
    F ⁡ ( - m , b c ; z ) = ( c - b ) m ( c ) m ⁢ F ⁡ ( - m , b b - c - m + 1 ; 1 - z ) = ( c - b ) m ( c ) m ⁢ z m ⁢ F ⁡ ( - m , 1 - c - m b - c - m + 1 ; 1 - 1 z ) , Gauss-hypergeometric-F 𝑚 𝑏 𝑐 𝑧 subscript 𝑐 𝑏 𝑚 subscript 𝑐 𝑚 Gauss-hypergeometric-F 𝑚 𝑏 𝑏 𝑐 𝑚 1 1 𝑧 subscript 𝑐 𝑏 𝑚 subscript 𝑐 𝑚 superscript 𝑧 𝑚 Gauss-hypergeometric-F 𝑚 1 𝑐 𝑚 𝑏 𝑐 𝑚 1 1 1 𝑧 {\displaystyle{\displaystyle F\left({-m,b\atop c};z\right)=\frac{(c-b)_{m}}{(c% )_{m}}F\left({-m,b\atop b-c-m+1};1-z\right)=\frac{(c-b)_{m}}{(c)_{m}}z^{m}F% \left({-m,1-c-m\atop b-c-m+1};1-\frac{1}{z}\right),}}
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    DLMF id
    DLMF:15.8.E7
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