DLMF:15.5.E18 (Q5035)

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DLMF:15.5.E18
No description defined

    Statements

    test
    c ⁢ ( c - 1 ) ⁢ ( z - 1 ) ⁢ F ⁡ ( a , b ; c - 1 ; z ) + c ⁢ ( c - 1 - ( 2 ⁢ c - a - b - 1 ) ⁢ z ) ⁢ F ⁡ ( a , b ; c ; z ) + ( c - a ) ⁢ ( c - b ) ⁢ z ⁢ F ⁡ ( a , b ; c + 1 ; z ) = 0 . 𝑐 𝑐 1 𝑧 1 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 1 𝑧 𝑐 𝑐 1 2 𝑐 𝑎 𝑏 1 𝑧 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 𝑐 𝑎 𝑐 𝑏 𝑧 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 1 𝑧 0 {\displaystyle{\displaystyle c(c-1)(z-1)F\left(a,b;c-1;z\right)+{c\left(c-1-(2% c-a-b-1)z\right)}F\left(a,b;c;z\right)+(c-a)(c-b)zF\left(a,b;c+1;z\right)=0.}}
    0 references
    DLMF id
    DLMF:15.5.E18
    0 references
    Symbols used
    $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function
    test
    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.m2apdec
    0 references
    Q11644
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1qdec
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    Q11645
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1pdec
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    Q11646
    test
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C15.S1.XMD5.m1pdec
    0 references
    Q11647
    test
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C15.S1.XMD6.m1pdec
    0 references
     
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