DLMF:16.11.E6 (Q5240): Difference between revisions

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Revision as of 15:53, 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 14:38, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / constraint
			${\displaystyle{\displaystyle|\operatorname{ph}\left(-z\right)|\leq\pi}}$ |\phase@{-z}|\leq\pi
		Property / constraint: ${\displaystyle{\displaystyle|\operatorname{ph}\left(-z\right)|\leq\pi}}$ / rank
			Normal rank
		Property / Symbols used
			gamma function
		Property / Symbols used: gamma function / rank
			Normal rank
		Property / Symbols used: gamma function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$ \EulerGamma@{\NVar{z}}
		Property / Symbols used: gamma function / qualifier
			xml-id: C5.S2.E1.m2aadec
		Property / Symbols used
			Q11125
		Property / Symbols used: Q11125 / rank
			Normal rank
		Property / Symbols used: Q11125 / qualifier
			Defining formula: ${\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{z}\right)}}$ \genhyperF{\NVar{p}}{\NVar{q}}@{\NVar{a_{1},\dots,a_{p}}}{\NVar{b_{1},\dots,b_{q}}}{\NVar{z}}
		Property / Symbols used: Q11125 / qualifier
			xml-id: C16.S2.m1adec
		Property / Symbols used
			the ratio of the circumference of a circle to its diameter
		Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
			Normal rank
		Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
			Defining formula: ${\displaystyle{\displaystyle\pi}}$ \cpi
		Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
			xml-id: C3.S12.E1.m2aadec
		Property / Symbols used
			Q10817
		Property / Symbols used: Q10817 / rank
			Normal rank
		Property / Symbols used: Q10817 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\operatorname{ph}}}$ \phase
		Property / Symbols used: Q10817 / qualifier
			xml-id: C1.S9.E7.m1adec
		Property / Symbols used
			Q11691
		Property / Symbols used: Q11691 / rank
			Normal rank
		Property / Symbols used: Q11691 / qualifier
			Defining formula: ${\displaystyle{\displaystyle q}}$ q
		Property / Symbols used: Q11691 / qualifier
			xml-id: C16.S1.XMD2.m1ddec
		Property / Symbols used
			Q11692
		Property / Symbols used: Q11692 / rank
			Normal rank
		Property / Symbols used: Q11692 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11692 / qualifier
			xml-id: C16.S1.XMD3.m1bdec
		Property / Symbols used
			Q11693
		Property / Symbols used: Q11693 / rank
			Normal rank
		Property / Symbols used: Q11693 / qualifier
			Defining formula: ${\displaystyle{\displaystyle a,a_{1},\ldots,a_{p}}}$ a,a_{1},\ldots,a_{p}
		Property / Symbols used: Q11693 / qualifier
			xml-id: C16.S1.XMD4.m1cdec
		Property / Symbols used
			Q11694
		Property / Symbols used: Q11694 / rank
			Normal rank
		Property / Symbols used: Q11694 / qualifier
			Defining formula: ${\displaystyle{\displaystyle b,b_{1},\ldots,b_{q}}}$ b,b_{1},\ldots,b_{q}
		Property / Symbols used: Q11694 / qualifier
			xml-id: C16.S1.XMD5.m1cdec
		Property / Symbols used
			formal infinite series (locally)
		Property / Symbols used: formal infinite series (locally) / rank
			Normal rank
		Property / Symbols used: formal infinite series (locally) / qualifier
			Defining formula: ${\displaystyle{\displaystyle H_{p,q}(z)}}$ H_{p,q}(z)
		Property / Symbols used: formal infinite series (locally) / qualifier
			xml-id: C16.S11.XMD2.m1adec

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Latest revision as of 14:38, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:16.11.E6	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\left({\textstyle\ifrac{\prod\limits_{\ell=1}^{q+1}\Gamma\left(a_{\ell}\right)}{\prod\limits_{\ell=1}^{q}\Gamma\left(b_{\ell}\right)}}\right){{}_{q+1}F_{q}}\left({a_{1},\dots,a_{q+1}\atop b_{1},\dots,b_{q}};z\right)=H_{q+1,q}(-z),}}$

0 references

DLMF id

DLMF:16.11.E6

0 references

constraint

${\displaystyle{\displaystyle|\operatorname{ph}\left(-z\right)|\leq\pi}}$

0 references

Symbols used

gamma function

Defining formula

${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$

xml-id

C5.S2.E1.m2aadec

0 references

Q11125

Defining formula

${\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{z}\right)}}$

xml-id

C16.S2.m1adec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

${\displaystyle{\displaystyle\pi}}$

xml-id

C3.S12.E1.m2aadec

0 references

Q10817

Defining formula

${\displaystyle{\displaystyle\operatorname{ph}}}$

xml-id

C1.S9.E7.m1adec

0 references

Q11691

Defining formula

${\displaystyle{\displaystyle q}}$

xml-id

C16.S1.XMD2.m1ddec

0 references

Q11692

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C16.S1.XMD3.m1bdec

0 references

Q11693

Defining formula

${\displaystyle{\displaystyle a,a_{1},\ldots,a_{p}}}$

xml-id

C16.S1.XMD4.m1cdec

0 references

Q11694

Defining formula

${\displaystyle{\displaystyle b,b_{1},\ldots,b_{q}}}$

xml-id

C16.S1.XMD5.m1cdec

0 references

formal infinite series (locally)

Defining formula

${\displaystyle{\displaystyle H_{p,q}(z)}}$

xml-id

C16.S11.XMD2.m1adec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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