DLMF:18.29.E2 (Q5997): Difference between revisions

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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.m1dec
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
Property / Symbols used
 
Property / Symbols used: Q11726 / rank
 
Normal rank
Property / Symbols used: Q11726 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11726 / qualifier
 
xml-id: C18.S1.XMD6.m1adec

Latest revision as of 13:25, 2 January 2020

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DLMF:18.29.E2
No description defined

    Statements

    Defining formula
    Q n ⁢ ( z ; a , b , c , d ∣ q ) ∼ z n ⁢ ( a ⁢ z - 1 , b ⁢ z - 1 , c ⁢ z - 1 , d ⁢ z - 1 ; q ) ∞ ( z - 2 , b ⁢ c , b ⁢ d , c ⁢ d ; q ) ∞ , asymptotically-equals subscript 𝑄 𝑛 𝑧 𝑎 𝑏 𝑐 conditional 𝑑 𝑞 superscript 𝑧 𝑛 q-multiple-Pochhammer 𝑎 superscript 𝑧 1 𝑏 superscript 𝑧 1 𝑐 superscript 𝑧 1 𝑑 superscript 𝑧 1 𝑞 q-multiple-Pochhammer superscript 𝑧 2 𝑏 𝑐 𝑏 𝑑 𝑐 𝑑 𝑞 {\displaystyle{\displaystyle Q_{n}(z;a,b,c,d\mid q)\sim\frac{z^{n}\left(az^{-1% },bz^{-1},cz^{-1},dz^{-1};q\right)_{\infty}}{\left(z^{-2},bc,bd,cd;q\right)_{% \infty}},}}
    0 references
    DLMF id
    DLMF:18.29.E2
    0 references
    constraint
    z , a , b , c , d , q 𝑧 𝑎 𝑏 𝑐 𝑑 𝑞 {\displaystyle{\displaystyle z,a,b,c,d,q}}
    0 references
    Symbols used
    asymptotic equality
    Defining formula
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2adec
    0 references
    Q11713
    Defining formula
    ( 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.m6aadec
    0 references
    Q11750
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C18.S1.XMD2.m1dec
    0 references
    Q11728
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C18.S1.XMD3.m1adec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1adec
    0 references
     
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