DLMF:17.9.E4 (Q5430): Difference between revisions

From testwiki
Jump to navigation Jump to search
← Older edit
imported>Admin
imported>Admin
 
(3 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: basic hypergeometric (or $$q$$ -hypergeometric) function / rank
 
Normal rank
Property / Symbols used: basic hypergeometric (or $$q$$ -hypergeometric) function / qualifier
 
test:

ϕ s r + 1 ⁡ ( a 0 , … , a r ; b 1 , … , b s ; q , z ) q-hypergeometric-rphis 𝑟 1 𝑠 subscript 𝑎 0 … subscript 𝑎 𝑟 subscript 𝑏 1 … subscript 𝑏 𝑠 𝑞 𝑧 {\displaystyle{\displaystyle{{}_{\NVar{r+1}}\phi_{\NVar{s}}}\left(\NVar{a_{0},% \dots,a_{r}};\NVar{b_{1},\dots,b_{s}};\NVar{q},\NVar{z}\right)}}

\qgenhyperphi{\NVar{r+1}}{\NVar{s}}@{\NVar{a_{0},\dots,a_{r}}}{\NVar{b_{1},\dots,b_{s}}}{\NVar{q}}{\NVar{z}}
Property / Symbols used: basic hypergeometric (or $$q$$ -hypergeometric) function / qualifier
 
xml-id: C17.S4.E1.m2acdec
Property / Symbols used
 
Property / Symbols used: Q11710 / rank
 
Normal rank
Property / Symbols used: Q11710 / qualifier
 
test:

q 𝑞 {\displaystyle{\displaystyle q}}

q
Property / Symbols used: Q11710 / qualifier
 
xml-id: C17.S1.XMD10.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11711 / rank
 
Normal rank
Property / Symbols used: Q11711 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11711 / qualifier
 
xml-id: C17.S1.XMD4.m1adec
Property / Symbols used
 
Property / Symbols used: Q11718 / rank
 
Normal rank
Property / Symbols used: Q11718 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11718 / qualifier
 
xml-id: C17.S1.XMD7.m1cdec

Latest revision as of 14:06, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:17.9.E4
No description defined

    Statements

    test
    ϕ 1 2 ⁡ ( q - n , b c ; q , z ) = ( c / b ; q ) n ( c ; q ) n ⁢ ( b ⁢ z q ) n ⁢ ϕ 2 3 ⁡ ( q - n , q / z , q 1 - n / c b ⁢ q 1 - n / c , 0 ; q , q ) , q-hypergeometric-rphis 2 1 superscript 𝑞 𝑛 𝑏 𝑐 𝑞 𝑧 q-Pochhammer-symbol 𝑐 𝑏 𝑞 𝑛 q-Pochhammer-symbol 𝑐 𝑞 𝑛 superscript 𝑏 𝑧 𝑞 𝑛 q-hypergeometric-rphis 3 2 superscript 𝑞 𝑛 𝑞 𝑧 superscript 𝑞 1 𝑛 𝑐 𝑏 superscript 𝑞 1 𝑛 𝑐 0 𝑞 𝑞 {\displaystyle{\displaystyle{{}_{2}\phi_{1}}\left({q^{-n},b\atop c};q,z\right)% =\frac{\left(c/b;q\right)_{n}}{\left(c;q\right)_{n}}\left(\frac{bz}{q}\right)^% {n}{{}_{3}\phi_{2}}\left({q^{-n},q/z,q^{1-n}/c\atop bq^{1-n}/c,0};q,q\right),}}
    0 references
    DLMF id
    DLMF:17.9.E4
    0 references
    Symbols used
    Q11298
    test
    ( a ; q ) n q-Pochhammer-symbol 𝑎 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}
    xml-id
    C17.S2.SS1.p1.m2acdec
    0 references
    basic hypergeometric (or $$q$$ -hypergeometric) function
    test
    ϕ s r + 1 ⁡ ( a 0 , … , a r ; b 1 , … , b s ; q , z ) q-hypergeometric-rphis 𝑟 1 𝑠 subscript 𝑎 0 … subscript 𝑎 𝑟 subscript 𝑏 1 … subscript 𝑏 𝑠 𝑞 𝑧 {\displaystyle{\displaystyle{{}_{\NVar{r+1}}\phi_{\NVar{s}}}\left(\NVar{a_{0},% \dots,a_{r}};\NVar{b_{1},\dots,b_{s}};\NVar{q},\NVar{z}\right)}}
    xml-id
    C17.S4.E1.m2acdec
    0 references
    Q11710
    test
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1cdec
    0 references
    Q11711
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1adec
    0 references
    Q11718
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C17.S1.XMD7.m1cdec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q5430&oldid=31296"