DLMF:17.5.E2 (Q5364): Difference between revisions

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Property / constraint
 

| z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}

|z|<1
Property / constraint: | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q11298 / rank
 
Normal rank
Property / Symbols used: Q11298 / qualifier
 
Defining formula:

( a ; q ) n q-Pochhammer-symbol 𝑎 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}

\qPochhammer{\NVar{a}}{\NVar{q}}{\NVar{n}}
Property / Symbols used: Q11298 / qualifier
 
xml-id: C17.S2.SS1.p1.m2aadec
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.m2aadec
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.m1adec
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.m1adec

Latest revision as of 14:56, 2 January 2020

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DLMF:17.5.E2
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    Statements

    ϕ 0 1 ( a ; - ; q , z ) = ( a z ; q ) ( z ; q ) , q-hypergeometric-rphis 1 0 𝑎 𝑞 𝑧 q-Pochhammer-symbol 𝑎 𝑧 𝑞 q-Pochhammer-symbol 𝑧 𝑞 {\displaystyle{\displaystyle{{}_{1}\phi_{0}}\left(a;-;q,z\right)=\frac{\left(% az;q\right)_{\infty}}{\left(z;q\right)_{\infty}},}}
    0 references
    DLMF:17.5.E2
    0 references
    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
    0 references
    ( a ; q ) n q-Pochhammer-symbol 𝑎 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}
    C17.S2.SS1.p1.m2aadec
    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.m2aadec
    0 references
    q 𝑞 {\displaystyle{\displaystyle q}}
    C17.S1.XMD10.m1adec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C17.S1.XMD7.m1adec
    0 references