DLMF:32.10.E31 (Q10124)

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DLMF:32.10.E31
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    Statements

    DLMF defining formula
    ϕ ⁢ ( ζ ) = C 1 ⁢ F ⁡ ( b , - a ; b + c ; ζ ) + C 2 ⁢ ζ - b + 1 - c ⁢ F ⁡ ( - a - b - c + 1 , - c + 1 ; 2 - b - c ; ζ ) , italic-ϕ 𝜁 subscript 𝐶 1 Gauss-hypergeometric-F 𝑏 𝑎 𝑏 𝑐 𝜁 subscript 𝐶 2 superscript 𝜁 𝑏 1 𝑐 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 1 𝑐 1 2 𝑏 𝑐 𝜁 {\displaystyle{\displaystyle\phi(\zeta)=C_{1}F\left(b,-a;b+c;\zeta\right)+C_{2% }\zeta^{-b+1-c}\*F\left(-a-b-c+1,-c+1;2-b-c;\zeta\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.m2adec
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    a
    DLMF defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C32.S10.XMD22.m1cdec
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    b
    DLMF defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C32.S10.XMD23.m1bdec
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    c
    DLMF defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C32.S10.XMD24.m1bdec
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    function
    DLMF defining formula
    ϕ ⁢ ( z ) italic-ϕ 𝑧 {\displaystyle{\displaystyle\phi(z)}}
    xml-id
    C32.S10.XMD27.m1adec
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    constant
    DLMF defining formula
    C 𝐶 {\displaystyle{\displaystyle C}}
    xml-id
    C32.S10.XMD32.m1dec
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    Identifiers

     
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