DLMF:17.5.E4 (Q5366): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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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.m2acdec
Property / Symbols used
 
Property / Symbols used: Q11710 / rank
 
Normal rank
Property / Symbols used: Q11710 / qualifier
 
Defining formula:

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
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11711 / qualifier
 
xml-id: C17.S1.XMD4.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11718 / rank
 
Normal rank
Property / Symbols used: Q11718 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

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

Latest revision as of 14:57, 2 January 2020

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DLMF:17.5.E4
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    Statements

    ϕ 0 1 ( 0 ; - ; q , z ) = n = 0 z n ( q ; q ) n = 1 ( z ; q ) , q-hypergeometric-rphis 1 0 0 𝑞 𝑧 superscript subscript 𝑛 0 superscript 𝑧 𝑛 q-Pochhammer-symbol 𝑞 𝑞 𝑛 1 q-Pochhammer-symbol 𝑧 𝑞 {\displaystyle{\displaystyle{{}_{1}\phi_{0}}\left(0;-;q,z\right)=\sum_{n=0}^{% \infty}\frac{z^{n}}{\left(q;q\right)_{n}}=\frac{1}{\left(z;q\right)_{\infty}},}}
    0 references
    DLMF:17.5.E4
    0 references
    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
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    ( a ; q ) n q-Pochhammer-symbol 𝑎 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}
    C17.S2.SS1.p1.m2acdec
    0 references
    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)}}
    C17.S4.E1.m2acdec
    0 references
    q 𝑞 {\displaystyle{\displaystyle q}}
    C17.S1.XMD10.m1cdec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C17.S1.XMD4.m1bdec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C17.S1.XMD7.m1cdec
    0 references