DLMF:15.16.E5 (Q5182): Difference between revisions

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Revision as of 15:51, 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 14:27, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / constraint
			${\displaystyle{\displaystyle|\operatorname{ph}z|<\pi}}$ |\phase@@{z}|<\pi
		Property / constraint: ${\displaystyle{\displaystyle|\operatorname{ph}z|<\pi}}$ / rank
			Normal rank
		Property / constraint
			${\displaystyle{\displaystyle|\operatorname{ph}\left(1-z\right)|<\pi}}$ |\phase@{1-z}|<\pi
		Property / constraint: ${\displaystyle{\displaystyle|\operatorname{ph}\left(1-z\right)|<\pi}}$ / 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.m2adec
		Property / Symbols used
			$$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function
		Property / Symbols used: $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function / rank
			Normal rank
		Property / Symbols used: $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function / qualifier
			Defining formula: ${\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}$ \hyperF@{\NVar{a}}{\NVar{b}}{\NVar{c}}{\NVar{z}}
		Property / Symbols used: $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function / qualifier
			xml-id: C15.S2.E1.m2addec
		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.m2adec
		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
			Q11644
		Property / Symbols used: Q11644 / rank
			Normal rank
		Property / Symbols used: Q11644 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11644 / qualifier
			xml-id: C15.S1.XMD3.m1ddec

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Latest revision as of 14:27, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:15.16.E5	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle F\left({\frac{1}{2}+\lambda,-\frac{1}{2}-\nu\atop 1+\lambda+\mu};z\right)F\left({\frac{1}{2}-\lambda,\frac{1}{2}+\nu\atop 1+\nu+\mu};1-z\right)+F\left({\frac{1}{2}+\lambda,\frac{1}{2}-\nu\atop 1+\lambda+\mu};z\right)F\left({-\frac{1}{2}-\lambda,\frac{1}{2}+\nu\atop 1+\nu+\mu};1-z\right)-F\left({\frac{1}{2}+\lambda,\frac{1}{2}-\nu\atop 1+\lambda+\mu};z\right)F\left({\frac{1}{2}-\lambda,\frac{1}{2}+\nu\atop 1+\nu+\mu};1-z\right)=\frac{\Gamma\left(1+\lambda+\mu\right)\Gamma\left(1+\nu+\mu\right)}{\Gamma\left(\lambda+\mu+\nu+\frac{3}{2}\right)\Gamma\left(\frac{1}{2}+\nu\right)},}}$

0 references

DLMF id

DLMF:15.16.E5

0 references

constraint

${\displaystyle{\displaystyle|\operatorname{ph}z|<\pi}}$

0 references

${\displaystyle{\displaystyle|\operatorname{ph}\left(1-z\right)|<\pi}}$

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2adec

0 references

$$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function

Defining formula

${\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}$

xml-id

C15.S2.E1.m2addec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2adec

0 references

Q10817

Defining formula

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

xml-id

C1.S9.E7.m1adec

0 references

Q11644

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C15.S1.XMD3.m1ddec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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