DLMF:16.12.E1 (Q5246)

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DLMF:16.12.E1
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    Statements

    Defining formula
    F 1 0 ⁡ ( - ; a ; z ) ⁢ F 1 0 ⁡ ( - ; b ; z ) = F 3 2 ⁡ ( 1 2 ⁢ ( a + b ) , 1 2 ⁢ ( a + b - 1 ) a , b , a + b - 1 ; 4 ⁢ z ) . Gauss-hypergeometric-pFq 0 1 𝑎 𝑧 Gauss-hypergeometric-pFq 0 1 𝑏 𝑧 Gauss-hypergeometric-pFq 2 3 1 2 𝑎 𝑏 1 2 𝑎 𝑏 1 𝑎 𝑏 𝑎 𝑏 1 4 𝑧 {\displaystyle{\displaystyle{{}_{0}F_{1}}\left(-;a;z\right){{}_{0}F_{1}}\left(% -;b;z\right)={{}_{2}F_{3}}\left({\frac{1}{2}(a+b),\frac{1}{2}(a+b-1)\atop a,b,% a+b-1};4z\right).}}
    0 references
    DLMF id
    DLMF:16.12.E1
    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.m1adec
    0 references
    Q11692
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C16.S1.XMD3.m1dec
    0 references
     
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