DLMF:16.3.E7 (Q5194)

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DLMF:16.3.E7
No description defined

    Statements

    Defining formula
    F 2 3 ⁡ ( a 1 + 2 , a 2 , a 3 b 1 , b 2 ; z ) ⁢ a 1 ⁢ ( a 1 + 1 ) ⁢ ( 1 - z ) + F 2 3 ⁡ ( a 1 + 1 , a 2 , a 3 b 1 , b 2 ; z ) ⁢ a 1 ⁢ ( b 1 + b 2 - 3 ⁢ a 1 - 2 + z ⁢ ( 2 ⁢ a 1 - a 2 - a 3 + 1 ) ) + F 2 3 ⁡ ( a 1 , a 2 , a 3 b 1 , b 2 ; z ) ⁢ ( ( 2 ⁢ a 1 - b 1 ) ⁢ ( 2 ⁢ a 1 - b 2 ) + a 1 - a 1 2 - z ⁢ ( a 1 - a 2 ) ⁢ ( a 1 - a 3 ) ) - F 2 3 ⁡ ( a 1 - 1 , a 2 , a 3 b 1 , b 2 ; z ) ⁢ ( a 1 - b 1 ) ⁢ ( a 1 - b 2 ) = 0 . Gauss-hypergeometric-pFq 3 2 subscript 𝑎 1 2 subscript 𝑎 2 subscript 𝑎 3 subscript 𝑏 1 subscript 𝑏 2 𝑧 subscript 𝑎 1 subscript 𝑎 1 1 1 𝑧 Gauss-hypergeometric-pFq 3 2 subscript 𝑎 1 1 subscript 𝑎 2 subscript 𝑎 3 subscript 𝑏 1 subscript 𝑏 2 𝑧 subscript 𝑎 1 subscript 𝑏 1 subscript 𝑏 2 3 subscript 𝑎 1 2 𝑧 2 subscript 𝑎 1 subscript 𝑎 2 subscript 𝑎 3 1 Gauss-hypergeometric-pFq 3 2 subscript 𝑎 1 subscript 𝑎 2 subscript 𝑎 3 subscript 𝑏 1 subscript 𝑏 2 𝑧 2 subscript 𝑎 1 subscript 𝑏 1 2 subscript 𝑎 1 subscript 𝑏 2 subscript 𝑎 1 superscript subscript 𝑎 1 2 𝑧 subscript 𝑎 1 subscript 𝑎 2 subscript 𝑎 1 subscript 𝑎 3 Gauss-hypergeometric-pFq 3 2 subscript 𝑎 1 1 subscript 𝑎 2 subscript 𝑎 3 subscript 𝑏 1 subscript 𝑏 2 𝑧 subscript 𝑎 1 subscript 𝑏 1 subscript 𝑎 1 subscript 𝑏 2 0 {\displaystyle{\displaystyle{{}_{3}F_{2}}\left({a_{1}+2,a_{2},a_{3}\atop b_{1}% ,b_{2}};z\right)a_{1}(a_{1}+1)(1-z)+{{}_{3}F_{2}}\left({a_{1}+1,a_{2},a_{3}% \atop b_{1},b_{2}};z\right)a_{1}\left(b_{1}+b_{2}-3a_{1}-2+z(2a_{1}-a_{2}-a_{3% }+1)\right)+{{}_{3}F_{2}}\left({a_{1},a_{2},a_{3}\atop b_{1},b_{2}};z\right)% \left((2a_{1}-b_{1})(2a_{1}-b_{2})+a_{1}-a_{1}^{2}-z(a_{1}-a_{2})(a_{1}-a_{3})% \right)-{{}_{3}F_{2}}\left({a_{1}-1,a_{2},a_{3}\atop b_{1},b_{2}};z\right)(a_{% 1}-b_{1})(a_{1}-b_{2})=0.}}
    0 references
    DLMF id
    DLMF:16.3.E7
    0 references
    Symbols used
    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.m1aedec
    0 references
    Q11692
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C16.S1.XMD3.m1fdec
    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
    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.m1edec
    0 references
     
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