DLMF:5.13.E5 (Q2162): Difference between revisions

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Revision as of 13:13, 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 01:05, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / constraint
			${\displaystyle{\displaystyle\Re(a_{k})>0}}$ \realpart@@{(a_{k})}>0
		Property / constraint: ${\displaystyle{\displaystyle\Re(a_{k})>0}}$ / rank
			Normal rank
		Property / constraint
			${\displaystyle{\displaystyle\Re(a_{k})>0}}$ \Re(a_{k})>0
		Property / constraint: ${\displaystyle{\displaystyle\Re(a_{k})>0}}$ / rank
			Normal rank
		Property / constraint
			${\displaystyle{\displaystyle k=1,2,3,4}}$ k=1,2,3,4
		Property / constraint: ${\displaystyle{\displaystyle k=1,2,3,4}}$ / 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.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.m2acdec
		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.m1addec
		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.m2acdec
		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.m3addec
		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.m1acdec
		Property / Symbols used
			Q11292
		Property / Symbols used: Q11292 / rank
			Normal rank
		Property / Symbols used: Q11292 / qualifier
			Defining formula: ${\displaystyle{\displaystyle j}}$ j
		Property / Symbols used: Q11292 / qualifier
			xml-id: C5.S1.XMD1.m1dec
		Property / Symbols used
			Q11279
		Property / Symbols used: Q11279 / rank
			Normal rank
		Property / Symbols used: Q11279 / qualifier
			Defining formula: ${\displaystyle{\displaystyle k}}$ k
		Property / Symbols used: Q11279 / qualifier
			xml-id: C5.S1.XMD4.m1dec
		Property / Symbols used
			Q11275
		Property / Symbols used: Q11275 / rank
			Normal rank
		Property / Symbols used: Q11275 / qualifier
			Defining formula: ${\displaystyle{\displaystyle a}}$ a
		Property / Symbols used: Q11275 / qualifier
			xml-id: C5.S1.XMD8.m1ddec

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Latest revision as of 01:05, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:5.13.E5	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\frac{1}{4\pi}\int_{-\infty}^{\infty}\frac{\prod_{k=1}^{4}\Gamma\left(a_{k}+it\right)\Gamma\left(a_{k}-it\right)}{\Gamma\left(2it\right)\Gamma\left(-2it\right)}\mathrm{d}t=\frac{\prod_{1\leq j<k\leq 4}\Gamma\left(a_{j}+a_{k}\right)}{\Gamma\left(a_{1}+a_{2}+a_{3}+a_{4}\right)},}}$

0 references

DLMF id

DLMF:5.13.E5

0 references

constraint

${\displaystyle{\displaystyle\Re(a_{k})>0}}$

0 references

${\displaystyle{\displaystyle\Re(a_{k})>0}}$

0 references

${\displaystyle{\displaystyle k=1,2,3,4}}$

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.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.m2acdec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1addec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2acdec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3addec

0 references

Q10811

Defining formula

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

xml-id

C1.S9.E2.m1acdec

0 references

Q11292

Defining formula

${\displaystyle{\displaystyle j}}$

xml-id

C5.S1.XMD1.m1dec

0 references

Q11279

Defining formula

${\displaystyle{\displaystyle k}}$

xml-id

C5.S1.XMD4.m1dec

0 references

Q11275

Defining formula

${\displaystyle{\displaystyle a}}$

xml-id

C5.S1.XMD8.m1ddec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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