DLMF:18.27.E24 (Q5975): Difference between revisions

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Revision as of 17:35, 29 December 2019 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Created a new Item: Wikidata Toolkit example test item creation		Latest revision as of 01:52, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / constraint
			${\displaystyle{\displaystyle c>0}}$ c>0
		Property / constraint: ${\displaystyle{\displaystyle c>0}}$ / rank
			Normal rank
		Property / Symbols used
			Q10768
		Property / Symbols used: Q10768 / rank
			Normal rank
		Property / Symbols used: Q10768 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}$ \Kroneckerdelta{\NVar{j}}{\NVar{k}}
		Property / Symbols used: Q10768 / qualifier
			xml-id: introduction.Sx4.p1.t1.r4.m5ahdec
		Property / Symbols used
			discrete $$q$$ -Hermite II polynomial
		Property / Symbols used: discrete $$q$$ -Hermite II polynomial / rank
			Normal rank
		Property / Symbols used: discrete $$q$$ -Hermite II polynomial / qualifier
			Defining formula: ${\displaystyle{\displaystyle\tilde{h}_{\NVar{n}}\left(\NVar{x};\NVar{q}\right)}}$ \discqHermitepolyhII{\NVar{n}}@{\NVar{x}}{\NVar{q}}
		Property / Symbols used: discrete $$q$$ -Hermite II polynomial / qualifier
			xml-id: C18.S27.E23.m2aadec
		Property / Symbols used
			Q11298
		Property / Symbols used: Q11298 / rank
			Normal rank
		Property / Symbols used: Q11298 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}$ \qPochhammer{\NVar{a}}{\NVar{q}}{\NVar{n}}
		Property / Symbols used: Q11298 / qualifier
			xml-id: C17.S2.SS1.p1.m2ajdec
		Property / Symbols used
			Q11713
		Property / Symbols used: Q11713 / rank
			Normal rank
		Property / Symbols used: Q11713 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\left(\NVar{a_{1},a_{2},\dots,a_{r}};\NVar{q}\right)_{\NVar{n}}}}$ \qmultiPochhammersym{\NVar{a_{1},a_{2},\dots,a_{r}}}{\NVar{q}}{\NVar{n}}
		Property / Symbols used: Q11713 / qualifier
			xml-id: C17.S2.SS1.p1.m6acdec
		Property / Symbols used
			Q11728
		Property / Symbols used: Q11728 / rank
			Normal rank
		Property / Symbols used: Q11728 / qualifier
			Defining formula: ${\displaystyle{\displaystyle q}}$ q
		Property / Symbols used: Q11728 / qualifier
			xml-id: C18.S1.XMD3.m1vdec
		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.m1fdec
		Property / Symbols used
			Q11730
		Property / Symbols used: Q11730 / rank
			Normal rank
		Property / Symbols used: Q11730 / qualifier
			Defining formula: ${\displaystyle{\displaystyle m}}$ m
		Property / Symbols used: Q11730 / qualifier
			xml-id: C18.S1.XMD5.m1hdec
		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.m1sdec

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Latest revision as of 01:52, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:18.27.E24	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\sum_{\ell=-\infty}^{\infty}\left(\tilde{h}_{n}\left(cq^{\ell};q\right)\tilde{h}_{m}\left(cq^{\ell};q\right)+\tilde{h}_{n}\left(-cq^{\ell};q\right)\tilde{h}_{m}\left(-cq^{\ell};q\right)\right)\frac{q^{\ell}}{\left(-c^{2}q^{2\ell};q^{2}\right)_{\infty}}=2\frac{\left(q^{2},-c^{2}q,-c^{-2}q;q^{2}\right)_{\infty}}{\left(q,-c^{2},-c^{-2}q^{2};q^{2}\right)_{\infty}}\frac{\left(q;q\right)_{n}}{q^{n^{2}}}\delta_{n,m},}}$

0 references

DLMF id

DLMF:18.27.E24

0 references

constraint

${\displaystyle{\displaystyle c>0}}$

0 references

Symbols used

Q10768

Defining formula

${\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}$

xml-id

introduction.Sx4.p1.t1.r4.m5ahdec

0 references

discrete $$q$$ -Hermite II polynomial

Defining formula

${\displaystyle{\displaystyle\tilde{h}_{\NVar{n}}\left(\NVar{x};\NVar{q}\right)}}$

xml-id

C18.S27.E23.m2aadec

0 references

Q11298

Defining formula

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

xml-id

C17.S2.SS1.p1.m2ajdec

0 references

Q11713

Defining formula

${\displaystyle{\displaystyle\left(\NVar{a_{1},a_{2},\dots,a_{r}};\NVar{q}\right)_{\NVar{n}}}}$

xml-id

C17.S2.SS1.p1.m6acdec

0 references

Q11728

Defining formula

${\displaystyle{\displaystyle q}}$

xml-id

C18.S1.XMD3.m1vdec

0 references

Q11744

Defining formula

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

xml-id

C18.S1.XMD4.m1fdec

0 references

Q11730

Defining formula

${\displaystyle{\displaystyle m}}$

xml-id

C18.S1.XMD5.m1hdec

0 references

Q11726

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C18.S1.XMD6.m1sdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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