DLMF:15.8.E14 (Q5071)

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DLMF:15.8.E14
No description defined

    Statements

    Defining formula
    F ⁡ ( a , b 2 ⁢ b ; z ) = ( 1 - z ) - a / 2 ⁢ F ⁡ ( 1 2 ⁢ a , b - 1 2 ⁢ a b + 1 2 ; z 2 4 ⁢ z - 4 ) , Gauss-hypergeometric-F 𝑎 𝑏 2 𝑏 𝑧 superscript 1 𝑧 𝑎 2 Gauss-hypergeometric-F 1 2 𝑎 𝑏 1 2 𝑎 𝑏 1 2 superscript 𝑧 2 4 𝑧 4 {\displaystyle{\displaystyle F\left({a,b\atop 2b};z\right)=\left(1-z\right)^{-% \ifrac{a}{2}}F\left({\tfrac{1}{2}a,b-\tfrac{1}{2}a\atop b+\tfrac{1}{2}};\frac{% z^{2}}{4z-4}\right),}}
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    DLMF id
    DLMF:15.8.E14
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    constraint
    | ph ⁡ ( 1 - z ) | < π phase 1 𝑧 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}\left(1-z\right)|<\pi}}
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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.m2acdec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ajdec
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    Q10817
    Defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1ajdec
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    Q11644
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1mdec
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    Q11645
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1ldec
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    Q11646
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C15.S1.XMD5.m1ldec
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