DLMF:15.14.E1 (Q5176): 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 14:26, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / constraint
			${\displaystyle{\displaystyle\min(\Re a,\Re b)>\Re s>0}}$ \min(\realpart@@{a},\realpart@@{b})>\realpart@@{s}>0
		Property / constraint: ${\displaystyle{\displaystyle\min(\Re a,\Re b)>\Re s>0}}$ / 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
			Q10770
		Property / Symbols used: Q10770 / rank
			Normal rank
		Property / Symbols used: Q10770 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$ \diff{\NVar{x}}
		Property / Symbols used: Q10770 / qualifier
			xml-id: C1.S4.SS4.m1adec
		Property / Symbols used
			Q10771
		Property / Symbols used: Q10771 / rank
			Normal rank
		Property / Symbols used: Q10771 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\int}}$ \int
		Property / Symbols used: Q10771 / qualifier
			xml-id: C1.S4.SS4.m3adec
		Property / Symbols used
			Q10811
		Property / Symbols used: Q10811 / rank
			Normal rank
		Property / Symbols used: Q10811 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\Re}}$ \realpart@@
		Property / Symbols used: Q10811 / qualifier
			xml-id: C1.S9.E2.m1adec
		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.m2adec
		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
			Q11648
		Property / Symbols used: Q11648 / rank
			Normal rank
		Property / Symbols used: Q11648 / qualifier
			Defining formula: ${\displaystyle{\displaystyle s}}$ s
		Property / Symbols used: Q11648 / qualifier
			xml-id: C15.S1.XMD11.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.m1dec
		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.m1dec
		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.m1dec

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Latest revision as of 14:26, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:15.14.E1	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\int_{0}^{\infty}x^{s-1}\mathbf{F}\left({a,b\atop c};-x\right)\mathrm{d}x=\frac{\Gamma\left(s\right)\Gamma\left(a-s\right)\Gamma\left(b-s\right)}{\Gamma\left(a\right)\Gamma\left(b\right)\Gamma\left(c-s\right)},}}$

0 references

DLMF id

DLMF:15.14.E1

0 references

constraint

${\displaystyle{\displaystyle\min(\Re a,\Re b)>\Re s>0}}$

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2adec

0 references

Q10770

Defining formula

${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$

xml-id

C1.S4.SS4.m1adec

0 references

Q10771

Defining formula

${\displaystyle{\displaystyle\int}}$

xml-id

C1.S4.SS4.m3adec

0 references

Q10811

Defining formula

${\displaystyle{\displaystyle\Re}}$

xml-id

C1.S9.E2.m1adec

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.m2adec

0 references

Q11649

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C15.S1.XMD1.m1dec

0 references

Q11648

Defining formula

${\displaystyle{\displaystyle s}}$

xml-id

C15.S1.XMD11.m1dec

0 references

Q11645

Defining formula

${\displaystyle{\displaystyle a}}$

xml-id

C15.S1.XMD4.m1dec

0 references

Q11646

Defining formula

${\displaystyle{\displaystyle b}}$

xml-id

C15.S1.XMD5.m1dec

0 references

Q11647

Defining formula

${\displaystyle{\displaystyle c}}$

xml-id

C15.S1.XMD6.m1dec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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