DLMF:15.5.E11 (Q5028)

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DLMF:15.5.E11
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    Statements

    Defining formula
    ( c - a ) ⁢ F ⁡ ( a - 1 , b ; c ; z ) + ( 2 ⁢ a - c + ( b - a ) ⁢ z ) ⁢ F ⁡ ( a , b ; c ; z ) + a ⁢ ( z - 1 ) ⁢ F ⁡ ( a + 1 , b ; c ; z ) = 0 , 𝑐 𝑎 Gauss-hypergeometric-F 𝑎 1 𝑏 𝑐 𝑧 2 𝑎 𝑐 𝑏 𝑎 𝑧 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 𝑎 𝑧 1 Gauss-hypergeometric-F 𝑎 1 𝑏 𝑐 𝑧 0 {\displaystyle{\displaystyle(c-a)F\left(a-1,b;c;z\right)+\left(2a-c+(b-a)z% \right)F\left(a,b;c;z\right)+a(z-1)F\left(a+1,b;c;z\right)=0,}}
    0 references
    DLMF id
    DLMF:15.5.E11
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