DLMF:18.33.E16 (Q6026): Difference between revisions

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Property / constraint
 

a 2 q 2 < 1 superscript 𝑎 2 superscript 𝑞 2 1 {\displaystyle{\displaystyle a^{2}q^{2}<1}}

a^{2}q^{2}<1
Property / constraint: a 2 q 2 < 1 superscript 𝑎 2 superscript 𝑞 2 1 {\displaystyle{\displaystyle a^{2}q^{2}<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: Q11729 / rank
 
Normal rank
Property / Symbols used: Q11729 / qualifier
 
Defining formula:

w ( x ) 𝑤 𝑥 {\displaystyle{\displaystyle w(x)}}

w(x)
Property / Symbols used: Q11729 / qualifier
 
xml-id: C18.S1.XMD10.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11750 / rank
 
Normal rank
Property / Symbols used: Q11750 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11750 / qualifier
 
xml-id: C18.S1.XMD2.m1ndec
Property / Symbols used
 
Property / Symbols used: Q11728 / rank
 
Normal rank
Property / Symbols used: Q11728 / qualifier
 
Defining formula:

q 𝑞 {\displaystyle{\displaystyle q}}

q
Property / Symbols used: Q11728 / qualifier
 
xml-id: C18.S1.XMD3.m1adec

Latest revision as of 13:28, 2 January 2020

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DLMF:18.33.E16
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    Statements

    w ( z ) = | ( q z ; q 2 ) / ( a q z ; q 2 ) | 2 , 𝑤 𝑧 q-Pochhammer-symbol 𝑞 𝑧 superscript 𝑞 2 q-Pochhammer-symbol 𝑎 𝑞 𝑧 superscript 𝑞 2 2 {\displaystyle{\displaystyle w(z)={\left|\left(qz;q^{2}\right)_{\infty}\Bigm{/% }\left(aqz;q^{2}\right)_{\infty}\right|^{2}},}}
    0 references
    DLMF:18.33.E16
    0 references
    a 2 q 2 < 1 superscript 𝑎 2 superscript 𝑞 2 1 {\displaystyle{\displaystyle a^{2}q^{2}<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
    w ( x ) 𝑤 𝑥 {\displaystyle{\displaystyle w(x)}}
    C18.S1.XMD10.m1ddec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C18.S1.XMD2.m1ndec
    0 references
    q 𝑞 {\displaystyle{\displaystyle q}}
    C18.S1.XMD3.m1adec
    0 references