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DLMF:15.4.E7 - MaRDI portal

DLMF:15.4.E7 (Q5688)

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DLMF:15.4.E7
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    Statements

    DLMF defining formula
    F ⁡ ( a , 1 2 + a ; 1 2 ; z 2 ) = 1 2 ⁢ ( ( 1 + z ) - 2 ⁢ a + ( 1 - z ) - 2 ⁢ a ) , Gauss-hypergeometric-F 𝑎 1 2 𝑎 1 2 superscript 𝑧 2 1 2 superscript 1 𝑧 2 𝑎 superscript 1 𝑧 2 𝑎 {\displaystyle{\displaystyle F\left(a,\tfrac{1}{2}+a;\tfrac{1}{2};z^{2}\right)% =\tfrac{1}{2}\left((1+z)^{-2a}+(1-z)^{-2a}\right),}}
    0 references
    Symbols used
    $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function
    DLMF 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.m2afdec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1fdec
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    real or complex parameter
    DLMF defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1adec
    0 references

    Identifiers

     
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