DLMF:17.9.E10 (Q5436): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
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
 
Defining formula:

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.m2aidec

Revision as of 15:06, 2 January 2020

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DLMF:17.9.E10
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    Statements

    Defining formula
    ϕ 2 3 ⁡ ( q - n , b , c d , e ; q , d ⁢ e ⁢ q n b ⁢ c ) = ( e / c ; q ) n ( e ; q ) n ⁢ ϕ 2 3 ⁡ ( q - n , c , d / b d , c ⁢ q 1 - n / e ; q , q ) . q-hypergeometric-rphis 3 2 superscript 𝑞 𝑛 𝑏 𝑐 𝑑 𝑒 𝑞 𝑑 𝑒 superscript 𝑞 𝑛 𝑏 𝑐 q-Pochhammer-symbol 𝑒 𝑐 𝑞 𝑛 q-Pochhammer-symbol 𝑒 𝑞 𝑛 q-hypergeometric-rphis 3 2 superscript 𝑞 𝑛 𝑐 𝑑 𝑏 𝑑 𝑐 superscript 𝑞 1 𝑛 𝑒 𝑞 𝑞 {\displaystyle{\displaystyle{{}_{3}\phi_{2}}\left({q^{-n},b,c\atop d,e};q,% \frac{deq^{n}}{bc}\right)=\frac{\left(e/c;q\right)_{n}}{\left(e;q\right)_{n}}{% {}_{3}\phi_{2}}\left({q^{-n},c,d/b\atop d,cq^{1-n}/e};q,q\right).}}
    0 references
    DLMF id
    DLMF:17.9.E10
    0 references
    Symbols used
    Q11298
    Defining formula
    ( 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.m2agdec
    0 references
    basic hypergeometric (or $$q$$ -hypergeometric) function
    Defining formula
    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.m2aidec
    0 references
     
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