DLMF:15.5.E19 (Q5036)

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DLMF:15.5.E19
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    Statements

    test
    z ⁢ ( 1 - z ) ⁢ ( a + 1 ) ⁢ ( b + 1 ) ⁢ F ⁡ ( a + 2 , b + 2 ; c + 2 ; z ) + ( c - ( a + b + 1 ) ⁢ z ) ⁢ ( c + 1 ) ⁢ F ⁡ ( a + 1 , b + 1 ; c + 1 ; z ) - c ⁢ ( c + 1 ) ⁢ F ⁡ ( a , b ; c ; z ) = 0 . 𝑧 1 𝑧 𝑎 1 𝑏 1 Gauss-hypergeometric-F 𝑎 2 𝑏 2 𝑐 2 𝑧 𝑐 𝑎 𝑏 1 𝑧 𝑐 1 Gauss-hypergeometric-F 𝑎 1 𝑏 1 𝑐 1 𝑧 𝑐 𝑐 1 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 0 {\displaystyle{\displaystyle{z(1-z)(a+1)(b+1)}F\left(a+2,b+2;c+2;z\right)+{(c-% (a+b+1)z)(c+1)}F\left(a+1,b+1;c+1;z\right)-{c(c+1)}F\left(a,b;c;z\right)=0.}}
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    DLMF id
    DLMF:15.5.E19
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