DLMF:16.4.E6 (Q5200): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11693 / rank
 
Normal rank
Property / Symbols used: Q11693 / qualifier
 
Defining formula:

a , a 1 , … , a p 𝑎 subscript 𝑎 1 … subscript 𝑎 𝑝 {\displaystyle{\displaystyle a,a_{1},\ldots,a_{p}}}

a,a_{1},\ldots,a_{p}
Property / Symbols used: Q11693 / qualifier
 
xml-id: C16.S1.XMD4.m1ddec

Revision as of 14:31, 2 January 2020

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DLMF:16.4.E6
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    Statements

    Defining formula
    F 2 3 ⁡ ( a , b , c 1 2 ⁢ ( a + b + 1 ) , 2 ⁢ c ; 1 ) = Γ ⁡ ( 1 2 ) ⁢ Γ ⁡ ( c + 1 2 ) ⁢ Γ ⁡ ( 1 2 ⁢ ( a + b + 1 ) ) ⁢ Γ ⁡ ( c + 1 2 ⁢ ( 1 - a - b ) ) Γ ⁡ ( 1 2 ⁢ ( a + 1 ) ) ⁢ Γ ⁡ ( 1 2 ⁢ ( b + 1 ) ) ⁢ Γ ⁡ ( c + 1 2 ⁢ ( 1 - a ) ) ⁢ Γ ⁡ ( c + 1 2 ⁢ ( 1 - b ) ) , Gauss-hypergeometric-pFq 3 2 𝑎 𝑏 𝑐 1 2 𝑎 𝑏 1 2 𝑐 1 Euler-Gamma 1 2 Euler-Gamma 𝑐 1 2 Euler-Gamma 1 2 𝑎 𝑏 1 Euler-Gamma 𝑐 1 2 1 𝑎 𝑏 Euler-Gamma 1 2 𝑎 1 Euler-Gamma 1 2 𝑏 1 Euler-Gamma 𝑐 1 2 1 𝑎 Euler-Gamma 𝑐 1 2 1 𝑏 {\displaystyle{\displaystyle{{}_{3}F_{2}}\left({a,b,c\atop\frac{1}{2}(a+b+1),2% c};1\right)=\frac{\Gamma\left(\frac{1}{2}\right)\Gamma\left(c+\frac{1}{2}% \right)\Gamma\left(\frac{1}{2}(a+b+1)\right)\Gamma\left(c+\frac{1}{2}(1-a-b)% \right)}{\Gamma\left(\frac{1}{2}(a+1)\right)\Gamma\left(\frac{1}{2}(b+1)\right% )\Gamma\left(c+\frac{1}{2}(1-a)\right)\Gamma\left(c+\frac{1}{2}(1-b)\right)},}}
    0 references
    DLMF id
    DLMF:16.4.E6
    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.m2abdec
    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.m1acdec
    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.m1ddec
    0 references
     
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