DLMF:15.4.E16 (Q5000)

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DLMF:15.4.E16
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    Statements

    Defining formula
    F ⁡ ( a , 1 - a ; 3 2 ; sin 2 ⁡ z ) = sin ⁡ ( ( 2 ⁢ a - 1 ) ⁢ z ) ( 2 ⁢ a - 1 ) ⁢ sin ⁡ z . Gauss-hypergeometric-F 𝑎 1 𝑎 3 2 2 𝑧 2 𝑎 1 𝑧 2 𝑎 1 𝑧 {\displaystyle{\displaystyle F\left(a,1-a;\tfrac{3}{2};{\sin^{2}}z\right)=% \frac{\sin\left((2a-1)z\right)}{(2a-1)\sin z}.}}
    0 references
    DLMF id
    DLMF:15.4.E16
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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.m2aodec
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    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2acdec
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    Q11644
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1odec
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    Q11645
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1jdec
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