DLMF:15.4.E8 (Q4992)

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DLMF:15.4.E8
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    Statements

    Defining formula
    F ⁡ ( a , 1 2 + a ; 1 2 ; - tan 2 ⁡ z ) = ( cos ⁡ z ) 2 ⁢ a ⁢ cos ⁡ ( 2 ⁢ a ⁢ z ) . Gauss-hypergeometric-F 𝑎 1 2 𝑎 1 2 2 𝑧 superscript 𝑧 2 𝑎 2 𝑎 𝑧 {\displaystyle{\displaystyle F\left(a,\tfrac{1}{2}+a;\tfrac{1}{2};-{\tan^{2}}z% \right)=(\cos z)^{2a}\cos\left(2az\right).}}
    0 references
    DLMF id
    DLMF:15.4.E8
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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.m2agdec
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    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2adec
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    tangent function
    Defining formula
    tan ⁡ z 𝑧 {\displaystyle{\displaystyle\tan\NVar{z}}}
    xml-id
    C4.S14.E4.m2adec
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    Q11644
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1gdec
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    Q11645
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1bdec
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