DLMF:16.4.E13 (Q5207)

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DLMF:16.4.E13
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    Statements

    Defining formula
    F 2 3 ⁡ ( a , b , c d , e ; 1 ) = c ⁢ ( e - a ) d ⁢ e ⁢ F 2 3 ⁡ ( a , b + 1 , c + 1 d + 1 , e + 1 ; 1 ) + d - c d ⁢ F 2 3 ⁡ ( a , b + 1 , c d + 1 , e ; 1 ) . Gauss-hypergeometric-pFq 3 2 𝑎 𝑏 𝑐 𝑑 𝑒 1 𝑐 𝑒 𝑎 𝑑 𝑒 Gauss-hypergeometric-pFq 3 2 𝑎 𝑏 1 𝑐 1 𝑑 1 𝑒 1 1 𝑑 𝑐 𝑑 Gauss-hypergeometric-pFq 3 2 𝑎 𝑏 1 𝑐 𝑑 1 𝑒 1 {\displaystyle{\displaystyle{{}_{3}F_{2}}\left({a,b,c\atop d,e};1\right)=% \dfrac{c(e-a)}{de}{{}_{3}F_{2}}\left({a,b+1,c+1\atop d+1,e+1};1\right)+\dfrac{% d-c}{d}{{}_{3}F_{2}}\left({a,b+1,c\atop d+1,e};1\right).}}
    0 references
    DLMF id
    DLMF:16.4.E13
    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.m1ajdec
    0 references
    Q11695
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C16.S4.XMD1.m1bdec
    0 references
    Q11696
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C16.S4.XMD2.m1bdec
    0 references
    Q11697
    Defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C16.S4.XMD3.m1bdec
    0 references
    Q11698
    Defining formula
    d 𝑑 {\displaystyle{\displaystyle d}}
    xml-id
    C16.S4.XMD4.m1bdec
    0 references
    Q11699
    Defining formula
    e 𝑒 {\displaystyle{\displaystyle e}}
    xml-id
    C16.S4.XMD5.m1bdec
    0 references
     
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