DLMF:15.16.E2 (Q5179)

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DLMF:15.16.E2
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    Statements

    Defining formula
    ( 1 - z ) a + b - c ⁢ F ⁡ ( 2 ⁢ a , 2 ⁢ b ; 2 ⁢ c - 1 ; z ) = ∑ s = 0 ∞ A s ⁢ z s , superscript 1 𝑧 𝑎 𝑏 𝑐 Gauss-hypergeometric-F 2 𝑎 2 𝑏 2 𝑐 1 𝑧 superscript subscript 𝑠 0 subscript 𝐴 𝑠 superscript 𝑧 𝑠 {\displaystyle{\displaystyle(1-z)^{a+b-c}F\left(2a,2b;2c-1;z\right)=\sum_{s=0}% ^{\infty}A_{s}z^{s},}}
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    DLMF id
    DLMF:15.16.E2
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    constraint
    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
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    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.m2aadec
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    Q11648
    Defining formula
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C15.S1.XMD11.m1adec
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    Q11644
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1adec
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    Q11645
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1adec
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    Q11646
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C15.S1.XMD5.m1adec
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    Q11647
    Defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C15.S1.XMD6.m1adec
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