DLMF:17.6.E4 (Q5371): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
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.m2abdec

Revision as of 14:57, 2 January 2020

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DLMF:17.6.E4
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    Statements

    Defining formula
    ϕ 1 2 ⁡ ( b 2 , b 2 / c c ; q 2 , c ⁢ q / b 2 ) = 1 2 ⁢ ( b 2 , q ; q 2 ) ∞ ( c , c ⁢ q / b 2 ; q 2 ) ∞ ⁢ ( ( c / b ; q ) ∞ ( b ; q ) ∞ + ( - c / b ; q ) ∞ ( - b ; q ) ∞ ) , q-hypergeometric-rphis 2 1 superscript 𝑏 2 superscript 𝑏 2 𝑐 𝑐 superscript 𝑞 2 𝑐 𝑞 superscript 𝑏 2 1 2 q-multiple-Pochhammer superscript 𝑏 2 𝑞 superscript 𝑞 2 q-multiple-Pochhammer 𝑐 𝑐 𝑞 superscript 𝑏 2 superscript 𝑞 2 q-Pochhammer-symbol 𝑐 𝑏 𝑞 q-Pochhammer-symbol 𝑏 𝑞 q-Pochhammer-symbol 𝑐 𝑏 𝑞 q-Pochhammer-symbol 𝑏 𝑞 {\displaystyle{\displaystyle{{}_{2}\phi_{1}}\left({b^{2},\ifrac{b^{2}}{c}\atop c% };q^{2},\ifrac{cq}{b^{2}}\right)=\frac{1}{2}\frac{\left(b^{2},q;q^{2}\right)_{% \infty}}{\left(c,cq/b^{2};q^{2}\right)_{\infty}}\left(\frac{\left(c/b;q\right)% _{\infty}}{\left(b;q\right)_{\infty}}+\frac{\left(-c/b;q\right)_{\infty}}{% \left(-b;q\right)_{\infty}}\right),}}
    0 references
    DLMF id
    DLMF:17.6.E4
    0 references
    constraint
    | c ⁢ q | < | b 2 | 𝑐 𝑞 superscript 𝑏 2 {\displaystyle{\displaystyle|cq|<|b^{2}|}}
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    Symbols used
    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.m2abdec
    0 references
     
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