DLMF:17.13.E1 (Q5466): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11299 / rank
 
Normal rank
Property / Symbols used: Q11299 / qualifier
 
Defining formula:

d q x q-differential 𝑞 𝑥 {\displaystyle{\displaystyle{\mathrm{d}}_{\NVar{q}}\NVar{x}}}

\qdiff{\NVar{q}}{\NVar{x}}
Property / Symbols used: Q11299 / qualifier
 
xml-id: C17.S2.SS5.p1.m3adec
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.m1dec
Property / Symbols used
 
Property / Symbols used: Q11719 / rank
 
Normal rank
Property / Symbols used: Q11719 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11719 / qualifier
 
xml-id: C17.S1.XMD8.m1dec

Latest revision as of 15:10, 2 January 2020

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DLMF:17.13.E1
No description defined

    Statements

    Defining formula
    ∫ - c d ( - q ⁢ x / c ; q ) ∞ ⁢ ( q ⁢ x / d ; q ) ∞ ( - a ⁢ x / c ; q ) ∞ ⁢ ( b ⁢ x / d ; q ) ∞ ⁢ d q x = ( 1 - q ) ⁢ ( q ; q ) ∞ ⁢ ( a ⁢ b ; q ) ∞ ⁢ c ⁢ d ⁢ ( - c / d ; q ) ∞ ⁢ ( - d / c ; q ) ∞ ( a ; q ) ∞ ⁢ ( b ; q ) ∞ ⁢ ( c + d ) ⁢ ( - b ⁢ c / d ; q ) ∞ ⁢ ( - a ⁢ d / c ; q ) ∞ , superscript subscript 𝑐 𝑑 q-Pochhammer-symbol 𝑞 𝑥 𝑐 𝑞 q-Pochhammer-symbol 𝑞 𝑥 𝑑 𝑞 q-Pochhammer-symbol 𝑎 𝑥 𝑐 𝑞 q-Pochhammer-symbol 𝑏 𝑥 𝑑 𝑞 q-differential 𝑞 𝑥 1 𝑞 q-Pochhammer-symbol 𝑞 𝑞 q-Pochhammer-symbol 𝑎 𝑏 𝑞 𝑐 𝑑 q-Pochhammer-symbol 𝑐 𝑑 𝑞 q-Pochhammer-symbol 𝑑 𝑐 𝑞 q-Pochhammer-symbol 𝑎 𝑞 q-Pochhammer-symbol 𝑏 𝑞 𝑐 𝑑 q-Pochhammer-symbol 𝑏 𝑐 𝑑 𝑞 q-Pochhammer-symbol 𝑎 𝑑 𝑐 𝑞 {\displaystyle{\displaystyle\int_{-c}^{d}\frac{\left(-qx/c;q\right)_{\infty}% \left(qx/d;q\right)_{\infty}}{\left(-ax/c;q\right)_{\infty}\left(bx/d;q\right)% _{\infty}}{\mathrm{d}}_{q}x=\frac{(1-q)\left(q;q\right)_{\infty}\left(ab;q% \right)_{\infty}cd\left(-c/d;q\right)_{\infty}\left(-d/c;q\right)_{\infty}}{% \left(a;q\right)_{\infty}\left(b;q\right)_{\infty}(c+d)\left(-bc/d;q\right)_{% \infty}\left(-ad/c;q\right)_{\infty}},}}
    0 references
    DLMF id
    DLMF:17.13.E1
    0 references
    Symbols used
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
    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.m2adec
    0 references
    Q11299
    Defining formula
    d q x q-differential 𝑞 𝑥 {\displaystyle{\displaystyle{\mathrm{d}}_{\NVar{q}}\NVar{x}}}
    xml-id
    C17.S2.SS5.p1.m3adec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1dec
    0 references
    Q11719
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C17.S1.XMD8.m1dec
    0 references
     
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