DLMF:18.27.E19 (Q5970): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1aadec

Revision as of 01:50, 2 January 2020

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DLMF:18.27.E19
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    0 S n ( x ; q ) S m ( x ; q ) ( - x , - q x - 1 ; q ) d x = ln ( q - 1 ) q n ( q ; q ) ( q ; q ) n δ n , m , superscript subscript 0 Stieltjes-Wigert-polynomial-S 𝑛 𝑥 𝑞 Stieltjes-Wigert-polynomial-S 𝑚 𝑥 𝑞 q-multiple-Pochhammer 𝑥 𝑞 superscript 𝑥 1 𝑞 𝑥 superscript 𝑞 1 superscript 𝑞 𝑛 q-Pochhammer-symbol 𝑞 𝑞 q-Pochhammer-symbol 𝑞 𝑞 𝑛 Kronecker 𝑛 𝑚 {\displaystyle{\displaystyle\int_{0}^{\infty}\frac{S_{n}\left(x;q\right)S_{m}% \left(x;q\right)}{\left(-x,-qx^{-1};q\right)_{\infty}}\mathrm{d}x=\frac{\ln% \left(q^{-1}\right)}{q^{n}}\frac{\left(q;q\right)_{\infty}}{\left(q;q\right)_{% n}}\delta_{n,m},}}
    0 references
    DLMF:18.27.E19
    0 references
    δ j , k Kronecker 𝑗 𝑘 {\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}
    introduction.Sx4.p1.t1.r4.m5aedec
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    S n ( x ; q ) Stieltjes-Wigert-polynomial-S 𝑛 𝑥 𝑞 {\displaystyle{\displaystyle S_{\NVar{n}}\left(\NVar{x};\NVar{q}\right)}}
    C18.S27.E18.m2aadec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1aadec
    0 references