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

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Revision as of 01:50, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 01:50, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / Symbols used
			Q11744
		Property / Symbols used: Q11744 / rank
			Normal rank
		Property / Symbols used: Q11744 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\ell}}$ \ell
		Property / Symbols used: Q11744 / qualifier
			xml-id: C18.S1.XMD4.m1bdec
		Property / Symbols used
			Q11726
		Property / Symbols used: Q11726 / rank
			Normal rank
		Property / Symbols used: Q11726 / qualifier
			Defining formula: ${\displaystyle{\displaystyle n}}$ n
		Property / Symbols used: Q11726 / qualifier
			xml-id: C18.S1.XMD6.m1mdec
		Property / Symbols used
			Q11727
		Property / Symbols used: Q11727 / rank
			Normal rank
		Property / Symbols used: Q11727 / qualifier
			Defining formula: ${\displaystyle{\displaystyle x}}$ x
		Property / Symbols used: Q11727 / qualifier
			xml-id: C18.S2.XMD3.m1ldec

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Latest revision as of 01:50, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:18.27.E18	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle S_{n}\left(x;q\right)=\sum_{\ell=0}^{n}\frac{q^{\ell^{2}}(-x)^{\ell}}{\left(q;q\right)_{\ell}\left(q;q\right)_{n-\ell}}=\frac{1}{\left(q;q\right)_{n}}{{}_{1}\phi_{1}}\left({q^{-n}\atop 0};q,-q^{n+1}x\right).}}$

0 references

DLMF id

DLMF:18.27.E18

0 references

Symbols defined

Stieltjes–Wigert polynomial

0 references

Symbols used

Q11298

Defining formula

${\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}$

xml-id

C17.S2.SS1.p1.m2addec

0 references

basic hypergeometric (or $$q$$ -hypergeometric) function

Defining formula

${\displaystyle{\displaystyle{{}_{\NVar{r+1}}\phi_{\NVar{s}}}\left(\NVar{a_{0},\dots,a_{r}};\NVar{b_{1},\dots,b_{s}};\NVar{q},\NVar{z}\right)}}$

xml-id

C17.S4.E1.m2addec

0 references

Q11728

Defining formula

${\displaystyle{\displaystyle q}}$

xml-id

C18.S1.XMD3.m1pdec

0 references

Q11744

Defining formula

${\displaystyle{\displaystyle\ell}}$

xml-id

C18.S1.XMD4.m1bdec

0 references

Q11726

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C18.S1.XMD6.m1mdec

0 references

Q11727

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C18.S2.XMD3.m1ldec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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