DLMF:16.2.E3 (Q5185): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11125 / rank
 
Normal rank
Property / Symbols used: Q11125 / qualifier
 
test:

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)}}

\genhyperF{\NVar{p}}{\NVar{q}}@{\NVar{a_{1},\dots,a_{p}}}{\NVar{b_{1},\dots,b_{q}}}{\NVar{z}}
Property / Symbols used: Q11125 / qualifier
 
xml-id: C16.S2.m1aadec
Property / Symbols used
 
Property / Symbols used: Q10759 / rank
 
Normal rank
Property / Symbols used: Q10759 / qualifier
 
test:

( 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
Property / Symbols used
 
Property / Symbols used: Q11690 / rank
 
Normal rank
Property / Symbols used: Q11690 / qualifier
 
test:

p 𝑝 {\displaystyle{\displaystyle p}}

p
Property / Symbols used: Q11690 / qualifier
 
xml-id: C16.S1.XMD1.m1adec
Property / Symbols used
 
Property / Symbols used: Q11691 / rank
 
Normal rank
Property / Symbols used: Q11691 / qualifier
 
test:

q 𝑞 {\displaystyle{\displaystyle q}}

q
Property / Symbols used: Q11691 / qualifier
 
xml-id: C16.S1.XMD2.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11692 / rank
 
Normal rank
Property / Symbols used: Q11692 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11692 / qualifier
 
xml-id: C16.S1.XMD3.m1adec

Latest revision as of 13:28, 2 January 2020

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DLMF:16.2.E3
No description defined

    Statements

    test
    F q p + 1 ⁡ ( - m , 𝐚 𝐛 ; z ) = ( 𝐚 ) m ⁢ ( - z ) m ( 𝐛 ) m ⁢ F p q + 1 ⁡ ( - m , 1 - m - 𝐛 1 - m - 𝐚 ; ( - 1 ) p + q z ) Gauss-hypergeometric-pFq 𝑝 1 𝑞 𝑚 𝐚 𝐛 𝑧 Pochhammer 𝐚 𝑚 superscript 𝑧 𝑚 Pochhammer 𝐛 𝑚 Gauss-hypergeometric-pFq 𝑞 1 𝑝 𝑚 1 𝑚 𝐛 1 𝑚 𝐚 superscript 1 𝑝 𝑞 𝑧 {\displaystyle{\displaystyle{{}_{p+1}F_{q}}\left({-m,\mathbf{a}\atop\mathbf{b}% };z\right)=\frac{{\left(\mathbf{a}\right)_{m}}(-z)^{m}}{{\left(\mathbf{b}% \right)_{m}}}{{}_{q+1}F_{p}}\left({-m,1-m-\mathbf{b}\atop 1-m-\mathbf{a}};% \frac{(-1)^{p+q}}{z}\right)}}
    0 references
    DLMF id
    DLMF:16.2.E3
    0 references
    Symbols used
    Q11125
    test
    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
    test
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1aadec
    0 references
    Q11690
    test
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C16.S1.XMD1.m1adec
    0 references
    Q11691
    test
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C16.S1.XMD2.m1bdec
    0 references
    Q11692
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C16.S1.XMD3.m1adec
    0 references
     
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