DLMF:15.5.E8 (Q5025)

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DLMF:15.5.E8
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    Statements

    Defining formula
    ( ( 1 - z ) ⁢ d d z ⁡ ( 1 - z ) ) n ⁢ ( z c - 1 ⁢ ( 1 - z ) b - c ⁢ F ⁡ ( a , b ; c ; z ) ) = ( c - n ) n ⁢ z c - n - 1 ⁢ ( 1 - z ) b - c + n ⁢ F ⁡ ( a - n , b ; c - n ; z ) . superscript 1 𝑧 derivative 𝑧 1 𝑧 𝑛 superscript 𝑧 𝑐 1 superscript 1 𝑧 𝑏 𝑐 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 Pochhammer 𝑐 𝑛 𝑛 superscript 𝑧 𝑐 𝑛 1 superscript 1 𝑧 𝑏 𝑐 𝑛 Gauss-hypergeometric-F 𝑎 𝑛 𝑏 𝑐 𝑛 𝑧 {\displaystyle{\displaystyle\left((1-z)\frac{\mathrm{d}}{\mathrm{d}z}(1-z)% \right)^{n}\left(z^{c-1}(1-z)^{b-c}F\left(a,b;c;z\right)\right)={\left(c-n% \right)_{n}}z^{c-n-1}(1-z)^{b-c+n}\*F\left(a-n,b;c-n;z\right).}}
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    DLMF id
    DLMF:15.5.E8
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