DLMF:16.4.E8 (Q5202): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10759 / rank
 
Normal rank
Property / Symbols used: Q10759 / qualifier
 
Defining formula:

( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}

\Pochhammersym{\NVar{a}}{\NVar{n}}
Property / Symbols used: Q10759 / qualifier
 
xml-id: C5.S2.SS3.m1aadec

Revision as of 14:31, 2 January 2020

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DLMF:16.4.E8
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    Statements

    Defining formula
    F 2 3 ⁡ ( - n , a , 1 - a d , 1 - d - 2 ⁢ n ; 1 ) = ( 1 2 ⁢ ( a + d ) ) n ⁢ ( 1 2 ⁢ ( d - a + 1 ) ) n ( 1 2 ⁢ d ) n ⁢ ( 1 2 ⁢ ( d + 1 ) ) n , Gauss-hypergeometric-pFq 3 2 𝑛 𝑎 1 𝑎 𝑑 1 𝑑 2 𝑛 1 Pochhammer 1 2 𝑎 𝑑 𝑛 Pochhammer 1 2 𝑑 𝑎 1 𝑛 Pochhammer 1 2 𝑑 𝑛 Pochhammer 1 2 𝑑 1 𝑛 {\displaystyle{\displaystyle{{}_{3}F_{2}}\left({-n,a,1-a\atop d,1-d-2n};1% \right)=\frac{{\left(\frac{1}{2}(a+d)\right)_{n}}{\left(\frac{1}{2}(d-a+1)% \right)_{n}}}{{\left(\frac{1}{2}d\right)_{n}}{\left(\frac{1}{2}(d+1)\right)_{n% }}},}}
    0 references
    DLMF id
    DLMF:16.4.E8
    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.m1aedec
    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
     
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