DLMF:15.16.E4 (Q5181)

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DLMF:15.16.E4
No description defined

    Statements

    Defining formula
    F ⁡ ( a , b c ; z ) ⁢ F ⁡ ( - a , - b - c ; z ) + a ⁢ b ⁢ ( a - c ) ⁢ ( b - c ) c 2 ⁢ ( 1 - c 2 ) ⁢ z 2 ⁢ F ⁡ ( 1 + a , 1 + b 2 + c ; z ) ⁢ F ⁡ ( 1 - a , 1 - b 2 - c ; z ) = 1 . Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 𝑎 𝑏 𝑎 𝑐 𝑏 𝑐 superscript 𝑐 2 1 superscript 𝑐 2 superscript 𝑧 2 Gauss-hypergeometric-F 1 𝑎 1 𝑏 2 𝑐 𝑧 Gauss-hypergeometric-F 1 𝑎 1 𝑏 2 𝑐 𝑧 1 {\displaystyle{\displaystyle F\left({a,b\atop c};z\right)F\left({-a,-b\atop-c}% ;z\right)+\frac{ab(a-c)(b-c)}{c^{2}(1-c^{2})}z^{2}F\left({1+a,1+b\atop 2+c};z% \right)F\left({1-a,1-b\atop 2-c};z\right)=1.}}
    0 references
    DLMF id
    DLMF:15.16.E4
    0 references
    Symbols used
    $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function
    Defining formula
    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)}}
    xml-id
    C15.S2.E1.m2acdec
    0 references
    Q11644
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1cdec
    0 references
    Q11645
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1cdec
    0 references
    Q11646
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C15.S1.XMD5.m1cdec
    0 references
    Q11647
    Defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C15.S1.XMD6.m1cdec
    0 references
     
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