DLMF:16.6.E2 (Q5217)

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DLMF:16.6.E2
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    Statements

    Defining formula
    F 2 3 ⁡ ( a , 2 ⁢ b - a - 1 , 2 - 2 ⁢ b + a b , a - b + 3 2 ; z 4 ) = ( 1 - z ) - a ⁢ F 2 3 ⁡ ( 1 3 ⁢ a , 1 3 ⁢ a + 1 3 , 1 3 ⁢ a + 2 3 b , a - b + 3 2 ; - 27 ⁢ z 4 ⁢ ( 1 - z ) 3 ) . Gauss-hypergeometric-pFq 3 2 𝑎 2 𝑏 𝑎 1 2 2 𝑏 𝑎 𝑏 𝑎 𝑏 3 2 𝑧 4 superscript 1 𝑧 𝑎 Gauss-hypergeometric-pFq 3 2 1 3 𝑎 1 3 𝑎 1 3 1 3 𝑎 2 3 𝑏 𝑎 𝑏 3 2 27 𝑧 4 superscript 1 𝑧 3 {\displaystyle{\displaystyle{{}_{3}F_{2}}\left({a,2b-a-1,2-2b+a\atop b,a-b+% \frac{3}{2}};\frac{z}{4}\right)=(1-z)^{-a}{{}_{3}F_{2}}\left({\frac{1}{3}a,% \frac{1}{3}a+\frac{1}{3},\frac{1}{3}a+\frac{2}{3}\atop b,a-b+\frac{3}{2}};% \frac{-27z}{4(1-z)^{3}}\right).}}
    0 references
    DLMF id
    DLMF:16.6.E2
    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.m1aadec
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