DLMF:16.8.E7 (Q5226): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
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.m1bdec

Revision as of 14:35, 2 January 2020

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DLMF:16.8.E7
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    Statements

    Defining formula
    w ~ j ⁢ ( z ) = ( - z ) - a j ⁢ F q q + 1 ⁡ ( a j , 1 - b 1 + a j , … , 1 - b q + a j 1 - a 1 + a j , … * … , 1 - a q + 1 + a j ; 1 z ) , subscript ~ 𝑤 𝑗 𝑧 superscript 𝑧 subscript 𝑎 𝑗 Gauss-hypergeometric-pFq 𝑞 1 𝑞 subscript 𝑎 𝑗 1 subscript 𝑏 1 subscript 𝑎 𝑗 … 1 subscript 𝑏 𝑞 subscript 𝑎 𝑗 1 subscript 𝑎 1 subscript 𝑎 𝑗 … … 1 subscript 𝑎 𝑞 1 subscript 𝑎 𝑗 1 𝑧 {\displaystyle{\displaystyle\widetilde{w}_{j}(z)=(-z)^{-a_{j}}{{}_{q+1}F_{q}}% \left({a_{j},1-b_{1}+a_{j},\dots,1-b_{q}+a_{j}\atop 1-a_{1}+a_{j},\ldots*\dots% ,1-a_{q+1}+a_{j}};\frac{1}{z}\right),}}
    0 references
    DLMF id
    DLMF:16.8.E7
    0 references
    constraint
    j = 1 , … , q + 1 𝑗 1 … 𝑞 1 {\displaystyle{\displaystyle j=1,\dots,q+1}}
    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
    Q11691
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C16.S1.XMD2.m1ddec
    0 references
    Q11692
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C16.S1.XMD3.m1fdec
    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.m1bdec
    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.m1bdec
    0 references
     
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