DLMF:15.4.E9 (Q4993)

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DLMF:15.4.E9
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    Statements

    Defining formula
    F ⁡ ( a , 1 2 + a ; 3 2 ; z 2 ) = 1 ( 2 - 4 ⁢ a ) ⁢ z ⁢ ( ( 1 + z ) 1 - 2 ⁢ a - ( 1 - z ) 1 - 2 ⁢ a ) , Gauss-hypergeometric-F 𝑎 1 2 𝑎 3 2 superscript 𝑧 2 1 2 4 𝑎 𝑧 superscript 1 𝑧 1 2 𝑎 superscript 1 𝑧 1 2 𝑎 {\displaystyle{\displaystyle F\left(a,\tfrac{1}{2}+a;\tfrac{3}{2};z^{2}\right)% =\frac{1}{(2-4a)z}\left((1+z)^{1-2a}-(1-z)^{1-2a}\right),}}
    0 references
    DLMF id
    DLMF:15.4.E9
    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.m2ahdec
    0 references
    Q11644
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1hdec
    0 references
    Q11645
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1cdec
    0 references
     
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