DLMF:15.2.E3 (Q4979): Difference between revisions

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Revision as of 15:44, 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 13:46, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / constraint
			${\displaystyle{\displaystyle x>1}}$ x>1
		Property / constraint: ${\displaystyle{\displaystyle x>1}}$ / 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.m2abdec
		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
			imaginary unit
		Property / Symbols used: imaginary unit / rank
			Normal rank
		Property / Symbols used: imaginary unit / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{i}}}$ \iunit
		Property / Symbols used: imaginary unit / qualifier
			xml-id: C1.S9.E1.m2adec
		Property / Symbols used
			$$={{}_{2}{\mathbf{F}}_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Olver’s hypergeometric function
		Property / Symbols used: $$={{}_{2}{\mathbf{F}}_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Olver’s hypergeometric function / rank
			Normal rank
		Property / Symbols used: $$={{}_{2}{\mathbf{F}}_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Olver’s hypergeometric function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathbf{F}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}$ \hyperOlverF@{\NVar{a}}{\NVar{b}}{\NVar{c}}{\NVar{z}}
		Property / Symbols used: $$={{}_{2}{\mathbf{F}}_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Olver’s hypergeometric function / qualifier
			xml-id: C15.S2.E2.m2aadec
		Property / Symbols used
			Q11649
		Property / Symbols used: Q11649 / rank
			Normal rank
		Property / Symbols used: Q11649 / qualifier
			Defining formula: ${\displaystyle{\displaystyle x}}$ x
		Property / Symbols used: Q11649 / qualifier
			xml-id: C15.S1.XMD1.m1dec
		Property / Symbols used
			Q11645
		Property / Symbols used: Q11645 / rank
			Normal rank
		Property / Symbols used: Q11645 / qualifier
			Defining formula: ${\displaystyle{\displaystyle a}}$ a
		Property / Symbols used: Q11645 / qualifier
			xml-id: C15.S1.XMD4.m1bdec
		Property / Symbols used
			Q11646
		Property / Symbols used: Q11646 / rank
			Normal rank
		Property / Symbols used: Q11646 / qualifier
			Defining formula: ${\displaystyle{\displaystyle b}}$ b
		Property / Symbols used: Q11646 / qualifier
			xml-id: C15.S1.XMD5.m1bdec
		Property / Symbols used
			Q11647
		Property / Symbols used: Q11647 / rank
			Normal rank
		Property / Symbols used: Q11647 / qualifier
			Defining formula: ${\displaystyle{\displaystyle c}}$ c
		Property / Symbols used: Q11647 / qualifier
			xml-id: C15.S1.XMD6.m1bdec

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Latest revision as of 13:46, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:15.2.E3	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\mathbf{F}\left({a,b\atop c};x+\mathrm{i}0\right)-\mathbf{F}\left({a,b\atop c};x-\mathrm{i}0\right)=\frac{2\pi\mathrm{i}}{\Gamma\left(a\right)\Gamma\left(b\right)}(x-1)^{c-a-b}\mathbf{F}\left({c-a,c-b\atop c-a-b+1};1-x\right),}}$

0 references

DLMF id

DLMF:15.2.E3

0 references

constraint

${\displaystyle{\displaystyle x>1}}$

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2abdec

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

imaginary unit

Defining formula

${\displaystyle{\displaystyle\mathrm{i}}}$

xml-id

C1.S9.E1.m2adec

0 references

$$={{}_{2}{\mathbf{F}}_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Olver’s hypergeometric function

Defining formula

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

xml-id

C15.S2.E2.m2aadec

0 references

Q11649

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C15.S1.XMD1.m1dec

0 references

Q11645

Defining formula

${\displaystyle{\displaystyle a}}$

xml-id

C15.S1.XMD4.m1bdec

0 references

Q11646

Defining formula

${\displaystyle{\displaystyle b}}$

xml-id

C15.S1.XMD5.m1bdec

0 references

Q11647

Defining formula

${\displaystyle{\displaystyle c}}$

xml-id

C15.S1.XMD6.m1bdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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