DLMF:16.4.E14 (Q5208): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11125 / rank
 
Normal rank
Property / Symbols used: Q11125 / qualifier
 
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)}}

\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.m1akdec
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.m1acdec
Property / Symbols used
 
Property / Symbols used: Q11695 / rank
 
Normal rank
Property / Symbols used: Q11695 / qualifier
 
Defining formula:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11695 / qualifier
 
xml-id: C16.S4.XMD1.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11696 / rank
 
Normal rank
Property / Symbols used: Q11696 / qualifier
 
Defining formula:

b 𝑏 {\displaystyle{\displaystyle b}}

b
Property / Symbols used: Q11696 / qualifier
 
xml-id: C16.S4.XMD2.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11697 / rank
 
Normal rank
Property / Symbols used: Q11697 / qualifier
 
Defining formula:

c 𝑐 {\displaystyle{\displaystyle c}}

c
Property / Symbols used: Q11697 / qualifier
 
xml-id: C16.S4.XMD3.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11698 / rank
 
Normal rank
Property / Symbols used: Q11698 / qualifier
 
Defining formula:

d 𝑑 {\displaystyle{\displaystyle d}}

d
Property / Symbols used: Q11698 / qualifier
 
xml-id: C16.S4.XMD4.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11699 / rank
 
Normal rank
Property / Symbols used: Q11699 / qualifier
 
Defining formula:

e 𝑒 {\displaystyle{\displaystyle e}}

e
Property / Symbols used: Q11699 / qualifier
 
xml-id: C16.S4.XMD5.m1cdec

Latest revision as of 14:32, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:16.4.E14
No description defined

    Statements

    Defining formula
    F 3 4 ⁡ ( - n , a , b , c d , e , f ; 1 ) = ( e - a ) n ⁢ ( f - a ) n ( e ) n ⁢ ( f ) n ⁢ F 3 4 ⁡ ( - n , a , d - b , d - c d , a - e - n + 1 , a - f - n + 1 ; 1 ) , Gauss-hypergeometric-pFq 4 3 𝑛 𝑎 𝑏 𝑐 𝑑 𝑒 𝑓 1 Pochhammer 𝑒 𝑎 𝑛 Pochhammer 𝑓 𝑎 𝑛 Pochhammer 𝑒 𝑛 Pochhammer 𝑓 𝑛 Gauss-hypergeometric-pFq 4 3 𝑛 𝑎 𝑑 𝑏 𝑑 𝑐 𝑑 𝑎 𝑒 𝑛 1 𝑎 𝑓 𝑛 1 1 {\displaystyle{\displaystyle{{}_{4}F_{3}}\left({-n,a,b,c\atop d,e,f};1\right)=% \frac{{\left(e-a\right)_{n}}{\left(f-a\right)_{n}}}{{\left(e\right)_{n}}{\left% (f\right)_{n}}}{{}_{4}F_{3}}\left({-n,a,d-b,d-c\atop d,a-e-n+1,a-f-n+1};1% \right),}}
    0 references
    DLMF id
    DLMF:16.4.E14
    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.m1akdec
    0 references
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1acdec
    0 references
    Q11695
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C16.S4.XMD1.m1cdec
    0 references
    Q11696
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C16.S4.XMD2.m1cdec
    0 references
    Q11697
    Defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C16.S4.XMD3.m1cdec
    0 references
    Q11698
    Defining formula
    d 𝑑 {\displaystyle{\displaystyle d}}
    xml-id
    C16.S4.XMD4.m1cdec
    0 references
    Q11699
    Defining formula
    e 𝑒 {\displaystyle{\displaystyle e}}
    xml-id
    C16.S4.XMD5.m1cdec
    0 references
     
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