DLMF:15.4.E23 (Q5007)

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DLMF:15.4.E23
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    Statements

    test
    lim z → 1 - ⁡ F ⁡ ( a , b ; c ; z ) ( 1 - z ) c - a - b = Γ ⁡ ( c ) ⁢ Γ ⁡ ( a + b - c ) Γ ⁡ ( a ) ⁢ Γ ⁡ ( b ) . subscript → 𝑧 limit-from 1 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 superscript 1 𝑧 𝑐 𝑎 𝑏 Euler-Gamma 𝑐 Euler-Gamma 𝑎 𝑏 𝑐 Euler-Gamma 𝑎 Euler-Gamma 𝑏 {\displaystyle{\displaystyle\lim_{z\to 1-}\frac{F\left(a,b;c;z\right)}{(1-z)^{% c-a-b}}=\frac{\Gamma\left(c\right)\Gamma\left(a+b-c\right)}{\Gamma\left(a% \right)\Gamma\left(b\right)}.}}
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    DLMF id
    DLMF:15.4.E23
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