DLMF:15.5.E12 (Q5029)

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DLMF:15.5.E12
No description defined

    Statements

    Defining formula
    ( b - a ) ⁢ F ⁡ ( a , b ; c ; z ) + a ⁢ F ⁡ ( a + 1 , b ; c ; z ) - b ⁢ F ⁡ ( a , b + 1 ; c ; z ) = 0 , 𝑏 𝑎 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 𝑎 Gauss-hypergeometric-F 𝑎 1 𝑏 𝑐 𝑧 𝑏 Gauss-hypergeometric-F 𝑎 𝑏 1 𝑐 𝑧 0 {\displaystyle{\displaystyle(b-a)F\left(a,b;c;z\right)+aF\left(a+1,b;c;z\right% )-bF\left(a,b+1;c;z\right)=0,}}
    0 references
    DLMF id
    DLMF:15.5.E12
    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.m2ajdec
    0 references
    Q11644
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1kdec
    0 references
    Q11645
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1jdec
    0 references
    Q11646
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C15.S1.XMD5.m1jdec
    0 references
    Q11647
    Defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C15.S1.XMD6.m1jdec
    0 references
     
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