DLMF:15.2.E6 (Q4983)

From DRMF
Revision as of 13:47, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:15.2.E6
No description defined

    Statements

    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
    DLMF id
    DLMF:15.2.E6
    0 references
    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
    0 references
    Q11644
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1ddec
    0 references
    Q11645
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1ddec
    0 references
    Q11646
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C15.S1.XMD5.m1edec
    0 references
    Q11652
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C15.S1.XMD8.m1adec
    0 references
    Q11651
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C15.S1.XMD9.m1bdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4983&oldid=40073"