DLMF:17.9.E3 (Q5429): 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.m2abdec
Property / Symbols used
 
Property / Symbols used: Q11713 / rank
 
Normal rank
Property / Symbols used: Q11713 / qualifier
 
test:

( a 1 , a 2 , … , a r ; q ) n q-multiple-Pochhammer subscript 𝑎 1 subscript 𝑎 2 … subscript 𝑎 𝑟 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a_{1},a_{2},\dots,a_{r}};\NVar{q}% \right)_{\NVar{n}}}}

\qmultiPochhammersym{\NVar{a_{1},a_{2},\dots,a_{r}}}{\NVar{q}}{\NVar{n}}
Property / Symbols used: Q11713 / qualifier
 
xml-id: C17.S2.SS1.p1.m6adec
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.m1bdec
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.m1bdec

Latest revision as of 14:05, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:17.9.E3
No description defined

    Statements

    test
    ϕ 1 2 ⁡ ( a , b c ; q , z ) = ( a ⁢ b ⁢ z / c ; q ) ∞ ( b ⁢ z / c ; q ) ∞ ⁢ ϕ 2 3 ⁡ ( a , c / b , 0 c , c ⁢ q / ( b ⁢ z ) ; q , q ) + ( a , b ⁢ z , c / b ; q ) ∞ ( c , z , c / ( b ⁢ z ) ; q ) ∞ ⁢ ϕ 2 3 ⁡ ( z , a ⁢ b ⁢ z / c , 0 b ⁢ z , b ⁢ z ⁢ q / c ; q , q ) , q-hypergeometric-rphis 2 1 𝑎 𝑏 𝑐 𝑞 𝑧 q-Pochhammer-symbol 𝑎 𝑏 𝑧 𝑐 𝑞 q-Pochhammer-symbol 𝑏 𝑧 𝑐 𝑞 q-hypergeometric-rphis 3 2 𝑎 𝑐 𝑏 0 𝑐 𝑐 𝑞 𝑏 𝑧 𝑞 𝑞 q-multiple-Pochhammer 𝑎 𝑏 𝑧 𝑐 𝑏 𝑞 q-multiple-Pochhammer 𝑐 𝑧 𝑐 𝑏 𝑧 𝑞 q-hypergeometric-rphis 3 2 𝑧 𝑎 𝑏 𝑧 𝑐 0 𝑏 𝑧 𝑏 𝑧 𝑞 𝑐 𝑞 𝑞 {\displaystyle{\displaystyle{{}_{2}\phi_{1}}\left({a,b\atop c};q,z\right)=% \frac{\left(abz/c;q\right)_{\infty}}{\left(bz/c;q\right)_{\infty}}{{}_{3}\phi_% {2}}\left({a,c/b,0\atop c,cq/(bz)};q,q\right)+\frac{\left(a,bz,c/b;q\right)_{% \infty}}{\left(c,z,c/(bz);q\right)_{\infty}}{{}_{3}\phi_{2}}\left({z,abz/c,0% \atop bz,bzq/c};q,q\right),}}
    0 references
    DLMF id
    DLMF:17.9.E3
    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.m2abdec
    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.m2abdec
    0 references
    Q11713
    test
    ( a 1 , a 2 , … , a r ; q ) n q-multiple-Pochhammer subscript 𝑎 1 subscript 𝑎 2 … subscript 𝑎 𝑟 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a_{1},a_{2},\dots,a_{r}};\NVar{q}% \right)_{\NVar{n}}}}
    xml-id
    C17.S2.SS1.p1.m6adec
    0 references
    Q11710
    test
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1bdec
    0 references
    Q11718
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C17.S1.XMD7.m1bdec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q5429&oldid=31290"