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DLMF:15.2.E6 - MaRDI portal

DLMF:15.2.E6 (Q5680)

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DLMF:15.2.E6
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    Statements

    DLMF defining formula
    F ⁡ ( - m , b - m - ℓ ; z ) = lim a → - m ⁡ F ⁡ ( a , b a - ℓ ; z ) , Gauss-hypergeometric-F 𝑚 𝑏 𝑚 ℓ 𝑧 subscript → 𝑎 𝑚 Gauss-hypergeometric-F 𝑎 𝑏 𝑎 ℓ 𝑧 {\displaystyle{\displaystyle F\left({-m,b\atop-m-\ell};z\right)=\lim_{a\to-m}F% \left({a,b\atop a-\ell};z\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.m2acdec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1ddec
    0 references
    real or complex parameter
    DLMF defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1ddec
    0 references
    real or complex parameter
    DLMF defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C15.S1.XMD5.m1edec
    0 references
    integer
    DLMF defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C15.S1.XMD8.m1adec
    0 references
    integer
    DLMF defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C15.S1.XMD9.m1bdec
    0 references

    Identifiers

     
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