DLMF:15.4.E26 (Q5010)

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DLMF:15.4.E26
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    Statements

    Defining formula
    F ⁡ ( a , b ; a - b + 1 ; - 1 ) = Γ ⁡ ( a - b + 1 ) ⁢ Γ ⁡ ( 1 2 ⁢ a + 1 ) Γ ⁡ ( a + 1 ) ⁢ Γ ⁡ ( 1 2 ⁢ a - b + 1 ) . Gauss-hypergeometric-F 𝑎 𝑏 𝑎 𝑏 1 1 Euler-Gamma 𝑎 𝑏 1 Euler-Gamma 1 2 𝑎 1 Euler-Gamma 𝑎 1 Euler-Gamma 1 2 𝑎 𝑏 1 {\displaystyle{\displaystyle F\left(a,b;a-b+1;-1\right)=\frac{\Gamma\left(a-b+% 1\right)\Gamma\left(\tfrac{1}{2}a+1\right)}{\Gamma\left(a+1\right)\Gamma\left(% \tfrac{1}{2}a-b+1\right)}.}}
    0 references
    DLMF id
    DLMF:15.4.E26
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    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aedec
    0 references
    $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ 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.m2axdec
    0 references
    Q11645
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1sdec
    0 references
    Q11646
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C15.S1.XMD5.m1hdec
    0 references
     
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