DLMF:5.14.E4 (Q2166): Difference between revisions

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Revision as of 01:05, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 01:06, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / Symbols used
			Q10815
		Property / Symbols used: Q10815 / rank
			Normal rank
		Property / Symbols used: Q10815 / qualifier
			Defining formula: ${\displaystyle{\displaystyle[\NVar{a},\NVar{b}]}}$ [\NVar{a},\NVar{b}]
		Property / Symbols used: Q10815 / qualifier
			xml-id: introduction.Sx4.p1.t1.r30.m6adec
		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.m1abdec
		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.m3abdec
		Property / Symbols used
			Q11276
		Property / Symbols used: Q11276 / rank
			Normal rank
		Property / Symbols used: Q11276 / qualifier
			Defining formula: ${\displaystyle{\displaystyle m}}$ m
		Property / Symbols used: Q11276 / qualifier
			xml-id: C5.S1.XMD2.m1dec
		Property / Symbols used
			Q11274
		Property / Symbols used: Q11274 / rank
			Normal rank
		Property / Symbols used: Q11274 / qualifier
			Defining formula: ${\displaystyle{\displaystyle n}}$ n
		Property / Symbols used: Q11274 / qualifier
			xml-id: C5.S1.XMD3.m1cdec
		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.m1bdec
		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.m1dec
		Property / Symbols used
			Q11283
		Property / Symbols used: Q11283 / rank
			Normal rank
		Property / Symbols used: Q11283 / qualifier
			Defining formula: ${\displaystyle{\displaystyle b}}$ b
		Property / Symbols used: Q11283 / qualifier
			xml-id: C5.S1.XMD9.m1dec
		Property / Symbols used
			product (locally)
		Property / Symbols used: product (locally) / rank
			Normal rank
		Property / Symbols used: product (locally) / qualifier
			Defining formula: ${\displaystyle{\displaystyle\Delta}}$ \Delta
		Property / Symbols used: product (locally) / qualifier
			xml-id: C5.S14.XMD2.m1adec

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Latest revision as of 01:06, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:5.14.E4	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\int_{[0,1]^{n}}t_{1}t_{2}\cdots t_{m}|\Delta(t_{1},\dots,t_{n})|^{2c}\prod_{k=1}^{n}t_{k}^{a-1}(1-t_{k})^{b-1}\mathrm{d}t_{k}=\frac{1}{(\Gamma\left(1+c\right))^{n}}\prod_{k=1}^{m}\frac{a+(n-k)c}{a+b+(2n-k-1)c}\*\prod_{k=1}^{n}\frac{\Gamma\left(a+(n-k)c\right)\Gamma\left(b+(n-k)c\right)\Gamma\left(1+kc\right)}{\Gamma\left(a+b+(2n-k-1)c\right)},}}$

0 references

DLMF id

DLMF:5.14.E4

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2abdec

0 references

Q10815

Defining formula

${\displaystyle{\displaystyle[\NVar{a},\NVar{b}]}}$

xml-id

introduction.Sx4.p1.t1.r30.m6adec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1abdec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3abdec

0 references

Q11276

Defining formula

${\displaystyle{\displaystyle m}}$

xml-id

C5.S1.XMD2.m1dec

0 references

Q11274

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C5.S1.XMD3.m1cdec

0 references

Q11279

Defining formula

${\displaystyle{\displaystyle k}}$

xml-id

C5.S1.XMD4.m1bdec

0 references

Q11275

Defining formula

${\displaystyle{\displaystyle a}}$

xml-id

C5.S1.XMD8.m1dec

0 references

Q11283

Defining formula

${\displaystyle{\displaystyle b}}$

xml-id

C5.S1.XMD9.m1dec

0 references

product (locally)

Defining formula

${\displaystyle{\displaystyle\Delta}}$

xml-id

C5.S14.XMD2.m1adec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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