DLMF:16.4.E10 (Q5204): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11694 / rank
 
Normal rank
Property / Symbols used: Q11694 / qualifier
 
Defining formula:

b , b 1 , … , b q 𝑏 subscript 𝑏 1 … subscript 𝑏 𝑞 {\displaystyle{\displaystyle b,b_{1},\ldots,b_{q}}}

b,b_{1},\ldots,b_{q}
Property / Symbols used: Q11694 / qualifier
 
xml-id: C16.S1.XMD5.m1gdec

Latest revision as of 14:31, 2 January 2020

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DLMF:16.4.E10
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    Statements

    Defining formula
    F 6 7 ⁡ ( a , 1 2 ⁢ a + 1 , b , c , d , f , - n 1 2 ⁢ a , a - b + 1 , a - c + 1 , a - d + 1 , a - f + 1 , a + n + 1 ; 1 ) = ( a + 1 ) n ⁢ ( a - b - c + 1 ) n ⁢ ( a - b - d + 1 ) n ⁢ ( a - c - d + 1 ) n ( a - b + 1 ) n ⁢ ( a - c + 1 ) n ⁢ ( a - d + 1 ) n ⁢ ( a - b - c - d + 1 ) n , Gauss-hypergeometric-pFq 7 6 𝑎 1 2 𝑎 1 𝑏 𝑐 𝑑 𝑓 𝑛 1 2 𝑎 𝑎 𝑏 1 𝑎 𝑐 1 𝑎 𝑑 1 𝑎 𝑓 1 𝑎 𝑛 1 1 Pochhammer 𝑎 1 𝑛 Pochhammer 𝑎 𝑏 𝑐 1 𝑛 Pochhammer 𝑎 𝑏 𝑑 1 𝑛 Pochhammer 𝑎 𝑐 𝑑 1 𝑛 Pochhammer 𝑎 𝑏 1 𝑛 Pochhammer 𝑎 𝑐 1 𝑛 Pochhammer 𝑎 𝑑 1 𝑛 Pochhammer 𝑎 𝑏 𝑐 𝑑 1 𝑛 {\displaystyle{\displaystyle{{}_{7}F_{6}}\left({a,\frac{1}{2}a+1,b,c,d,f,-n% \atop\frac{1}{2}a,a-b+1,a-c+1,a-d+1,a-f+1,a+n+1};1\right)=\frac{{\left(a+1% \right)_{n}}{\left(a-b-c+1\right)_{n}}{\left(a-b-d+1\right)_{n}}{\left(a-c-d+1% \right)_{n}}}{{\left(a-b+1\right)_{n}}{\left(a-c+1\right)_{n}}{\left(a-d+1% \right)_{n}}{\left(a-b-c-d+1\right)_{n}}},}}
    0 references
    DLMF id
    DLMF:16.4.E10
    0 references
    constraint
    n = 0 , 1 , … 𝑛 0 1 … {\displaystyle{\displaystyle n=0,1,\dots}}
    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.m1agdec
    0 references
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1abdec
    0 references
    Q11693
    Defining formula
    a , a 1 , … , a p 𝑎 subscript 𝑎 1 … subscript 𝑎 𝑝 {\displaystyle{\displaystyle a,a_{1},\ldots,a_{p}}}
    xml-id
    C16.S1.XMD4.m1hdec
    0 references
    Q11694
    Defining formula
    b , b 1 , … , b q 𝑏 subscript 𝑏 1 … subscript 𝑏 𝑞 {\displaystyle{\displaystyle b,b_{1},\ldots,b_{q}}}
    xml-id
    C16.S1.XMD5.m1gdec
    0 references
     
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