DLMF:16.4.E12 (Q5206)

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DLMF:16.4.E12
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    test
    ( a - d ) ⁢ ( b - d ) ⁢ ( c - d ) ⁢ ( F 2 3 ⁡ ( a , b , c d + 1 , e ; 1 ) - F 2 3 ⁡ ( a , b , c d , e ; 1 ) ) + a ⁢ b ⁢ c ⁢ F 2 3 ⁡ ( a , b , c d , e ; 1 ) = d ⁢ ( d - 1 ) ⁢ ( a + b + c - d - e + 1 ) ⁢ ( F 2 3 ⁡ ( a , b , c d , e ; 1 ) - F 2 3 ⁡ ( a , b , c d - 1 , e ; 1 ) ) , 𝑎 𝑑 𝑏 𝑑 𝑐 𝑑 Gauss-hypergeometric-pFq 3 2 𝑎 𝑏 𝑐 𝑑 1 𝑒 1 Gauss-hypergeometric-pFq 3 2 𝑎 𝑏 𝑐 𝑑 𝑒 1 𝑎 𝑏 𝑐 Gauss-hypergeometric-pFq 3 2 𝑎 𝑏 𝑐 𝑑 𝑒 1 𝑑 𝑑 1 𝑎 𝑏 𝑐 𝑑 𝑒 1 Gauss-hypergeometric-pFq 3 2 𝑎 𝑏 𝑐 𝑑 𝑒 1 Gauss-hypergeometric-pFq 3 2 𝑎 𝑏 𝑐 𝑑 1 𝑒 1 {\displaystyle{\displaystyle(a-d)(b-d)(c-d)\left({{}_{3}F_{2}}\left({a,b,c% \atop d+1,e};1\right)-{{}_{3}F_{2}}\left({a,b,c\atop d,e};1\right)\right)+abc{% {}_{3}F_{2}}\left({a,b,c\atop d,e};1\right)=d(d-1)(a+b+c-d-e+1)\left({{}_{3}F_% {2}}\left({a,b,c\atop d,e};1\right)-{{}_{3}F_{2}}\left({a,b,c\atop d-1,e};1% \right)\right),}}
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    DLMF id
    DLMF:16.4.E12
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