DLMF:18.26.E2 (Q5932)

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DLMF:18.26.E2
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    Statements

    Defining formula
    S n ⁡ ( y 2 ; a , b , c ) ( a + b ) n ⁢ ( a + c ) n = F 2 3 ⁡ ( - n , a + i ⁢ y , a - i ⁢ y a + b , a + c ; 1 ) . continuous-dual-Hahn-S 𝑛 superscript 𝑦 2 𝑎 𝑏 𝑐 Pochhammer 𝑎 𝑏 𝑛 Pochhammer 𝑎 𝑐 𝑛 Gauss-hypergeometric-pFq 3 2 𝑛 𝑎 𝑖 𝑦 𝑎 𝑖 𝑦 𝑎 𝑏 𝑎 𝑐 1 {\displaystyle{\displaystyle\frac{S_{n}\left(y^{2};a,b,c\right)}{{\left(a+b% \right)_{n}}{\left(a+c\right)_{n}}}={{}_{3}F_{2}}\left({-n,a+iy,a-iy\atop a+b,% a+c};1\right).}}
    0 references
    DLMF id
    DLMF:18.26.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
    0 references
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1aadec
    0 references
    Q11784
    Defining formula
    S n ⁡ ( x ; a , b , c ) continuous-dual-Hahn-S 𝑛 𝑥 𝑎 𝑏 𝑐 {\displaystyle{\displaystyle S_{\NVar{n}}\left(\NVar{x};\NVar{a},\NVar{b},% \NVar{c}\right)}}
    xml-id
    C18.S25.T1.t1.r3.m2adec
    0 references
     
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