DLMF:15.5.E19 (Q5036)

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DLMF:15.5.E19
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    Statements

    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:15.5.E19
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    F ( a , b ; c ; z ) Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}
    C15.S2.E1.m2aqdec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C15.S1.XMD3.m1rdec
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    a 𝑎 {\displaystyle{\displaystyle a}}
    C15.S1.XMD4.m1qdec
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    b 𝑏 {\displaystyle{\displaystyle b}}
    C15.S1.XMD5.m1qdec
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    c 𝑐 {\displaystyle{\displaystyle c}}
    C15.S1.XMD6.m1qdec
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