DLMF:17.6.E15 (Q5382): Difference between revisions

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Revision as of 15:58, 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 14:59, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / constraint
			${\displaystyle{\displaystyle|z|<1,|bq|<|c|}}$ |z|<1,|bq|<|c|
		Property / constraint: ${\displaystyle{\displaystyle|z|<1,|bq|<|c|}}$ / rank
			Normal rank
		Property / Symbols used
			basic hypergeometric (or $$q$$ -hypergeometric) function
		Property / Symbols used: basic hypergeometric (or $$q$$ -hypergeometric) function / rank
			Normal rank
		Property / Symbols used: basic hypergeometric (or $$q$$ -hypergeometric) function / qualifier
			Defining formula: ${\displaystyle{\displaystyle{{}_{\NVar{r+1}}\phi_{\NVar{s}}}\left(\NVar{a_{0},\dots,a_{r}};\NVar{b_{1},\dots,b_{s}};\NVar{q},\NVar{z}\right)}}$ \qgenhyperphi{\NVar{r+1}}{\NVar{s}}@{\NVar{a_{0},\dots,a_{r}}}{\NVar{b_{1},\dots,b_{s}}}{\NVar{q}}{\NVar{z}}
		Property / Symbols used: basic hypergeometric (or $$q$$ -hypergeometric) function / qualifier
			xml-id: C17.S4.E1.m2andec
		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.m6akdec
		Property / Symbols used
			Q11710
		Property / Symbols used: Q11710 / rank
			Normal rank
		Property / Symbols used: Q11710 / qualifier
			Defining formula: ${\displaystyle{\displaystyle q}}$ q
		Property / Symbols used: Q11710 / qualifier
			xml-id: C17.S1.XMD10.m1ndec
		Property / Symbols used
			Q11718
		Property / Symbols used: Q11718 / rank
			Normal rank
		Property / Symbols used: Q11718 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11718 / qualifier
			xml-id: C17.S1.XMD7.m1hdec

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Latest revision as of 14:59, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:17.6.E15	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle{{}_{2}\phi_{1}}\left({a,b\atop c};q,z\right)=\frac{\left(abz/c,q/c;q\right)_{\infty}}{\left(az/c,q/a;q\right)_{\infty}}{{}_{2}\phi_{1}}\left({c/a,cq/(abz)\atop cq/(az)};q,bq/c\right)-\frac{\left(b,q/c,c/a,az/q,q^{2}/(az);q\right)_{\infty}}{\left(c/q,bq/c,q/a,az/c,cq/(az);q\right)_{\infty}}{{}_{2}\phi_{1}}\left({aq/c,bq/c\atop q^{2}/c};q,z\right),}}$

0 references

DLMF id

DLMF:17.6.E15

0 references

constraint

${\displaystyle{\displaystyle|z|<1,|bq|<|c|}}$

0 references

Symbols used

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.m2andec

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.m6akdec

0 references

Q11710

Defining formula

${\displaystyle{\displaystyle q}}$

xml-id

C17.S1.XMD10.m1ndec

0 references

Q11718

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C17.S1.XMD7.m1hdec

0 references

 

Sitelinks

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