DLMF:18.27.E18 (Q5969): Difference between revisions

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‎Changed an Item: Wikidata Toolkit example test statement addition
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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.m2addec

Revision as of 01:50, 2 January 2020

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DLMF:18.27.E18
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    Statements

    Defining formula
    S n ⁡ ( x ; q ) = ∑ ℓ = 0 n q ℓ 2 ⁢ ( - x ) ℓ ( q ; q ) ℓ ⁢ ( q ; q ) n - ℓ = 1 ( q ; q ) n ⁢ ϕ 1 1 ⁡ ( q - n 0 ; q , - q n + 1 ⁢ x ) . Stieltjes-Wigert-polynomial-S 𝑛 𝑥 𝑞 superscript subscript ℓ 0 𝑛 superscript 𝑞 superscript ℓ 2 superscript 𝑥 ℓ q-Pochhammer-symbol 𝑞 𝑞 ℓ q-Pochhammer-symbol 𝑞 𝑞 𝑛 ℓ 1 q-Pochhammer-symbol 𝑞 𝑞 𝑛 q-hypergeometric-rphis 1 1 superscript 𝑞 𝑛 0 𝑞 superscript 𝑞 𝑛 1 𝑥 {\displaystyle{\displaystyle S_{n}\left(x;q\right)=\sum_{\ell=0}^{n}\frac{q^{% \ell^{2}}(-x)^{\ell}}{\left(q;q\right)_{\ell}\left(q;q\right)_{n-\ell}}=\frac{% 1}{\left(q;q\right)_{n}}{{}_{1}\phi_{1}}\left({q^{-n}\atop 0};q,-q^{n+1}x% \right).}}
    0 references
    DLMF id
    DLMF:18.27.E18
    0 references
    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.m2addec
    0 references
     
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