DLMF:16.4.E4 (Q5198)

From DRMF
Revision as of 14:30, 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:16.4.E4
No description defined

    Statements

    Defining formula
    F 2 3 ⁡ ( a , b , c a - b + 1 , a - c + 1 ; 1 ) = Γ ⁡ ( 1 2 ⁢ a + 1 ) ⁢ Γ ⁡ ( a - b + 1 ) ⁢ Γ ⁡ ( a - c + 1 ) ⁢ Γ ⁡ ( 1 2 ⁢ a - b - c + 1 ) Γ ⁡ ( a + 1 ) ⁢ Γ ⁡ ( 1 2 ⁢ a - b + 1 ) ⁢ Γ ⁡ ( 1 2 ⁢ a - c + 1 ) ⁢ Γ ⁡ ( a - b - c + 1 ) , Gauss-hypergeometric-pFq 3 2 𝑎 𝑏 𝑐 𝑎 𝑏 1 𝑎 𝑐 1 1 Euler-Gamma 1 2 𝑎 1 Euler-Gamma 𝑎 𝑏 1 Euler-Gamma 𝑎 𝑐 1 Euler-Gamma 1 2 𝑎 𝑏 𝑐 1 Euler-Gamma 𝑎 1 Euler-Gamma 1 2 𝑎 𝑏 1 Euler-Gamma 1 2 𝑎 𝑐 1 Euler-Gamma 𝑎 𝑏 𝑐 1 {\displaystyle{\displaystyle{{}_{3}F_{2}}\left({a,b,c\atop a-b+1,a-c+1};1% \right)=\frac{\Gamma\left(\frac{1}{2}a+1\right)\Gamma\left(a-b+1\right)\Gamma% \left(a-c+1\right)\Gamma\left(\frac{1}{2}a-b-c+1\right)}{\Gamma\left(a+1\right% )\Gamma\left(\frac{1}{2}a-b+1\right)\Gamma\left(\frac{1}{2}a-c+1\right)\Gamma% \left(a-b-c+1\right)},}}
    0 references
    DLMF id
    DLMF:16.4.E4
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    Q11125
    Defining formula
    F q p ⁡ ( a 1 , … , a p ; b 1 , … , b q ; z ) Gauss-hypergeometric-pFq 𝑝 𝑞 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 𝑧 {\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots% ,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{z}\right)}}
    xml-id
    C16.S2.m1aadec
    0 references
    Q11693
    Defining formula
    a , a 1 , … , a p 𝑎 subscript 𝑎 1 … subscript 𝑎 𝑝 {\displaystyle{\displaystyle a,a_{1},\ldots,a_{p}}}
    xml-id
    C16.S1.XMD4.m1cdec
    0 references
    Q11694
    Defining formula
    b , b 1 , … , b q 𝑏 subscript 𝑏 1 … subscript 𝑏 𝑞 {\displaystyle{\displaystyle b,b_{1},\ldots,b_{q}}}
    xml-id
    C16.S1.XMD5.m1cdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5198&oldid=47898"