DLMF:5.20.E3 (Q2208): Difference between revisions

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Revision as of 01:11, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 01:12, 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
			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
			base of natural logarithm
		Property / Symbols used: base of natural logarithm / rank
			Normal rank
		Property / Symbols used: base of natural logarithm / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{e}}}$ \expe
		Property / Symbols used: base of natural logarithm / qualifier
			xml-id: C4.S2.E11.m2adec
		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
			Q10812
		Property / Symbols used: Q10812 / rank
			Normal rank
		Property / Symbols used: Q10812 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathbb{R}}}$ \Reals
		Property / Symbols used: Q10812 / qualifier
			xml-id: introduction.Sx4.p2.t1.r14.m2adec
		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.m1adec
		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.m1bdec
		Property / Symbols used
			Q11281
		Property / Symbols used: Q11281 / rank
			Normal rank
		Property / Symbols used: Q11281 / qualifier
			Defining formula: ${\displaystyle{\displaystyle x}}$ x
		Property / Symbols used: Q11281 / qualifier
			xml-id: C5.S1.XMD5.m1bdec
		Property / Symbols used
			Q11300
		Property / Symbols used: Q11300 / rank
			Normal rank
		Property / Symbols used: Q11300 / qualifier
			Defining formula: ${\displaystyle{\displaystyle W}}$ W
		Property / Symbols used: Q11300 / qualifier
			xml-id: C5.S20.XMD1.m1bdec
		Property / Symbols used
			Q11303
		Property / Symbols used: Q11303 / rank
			Normal rank
		Property / Symbols used: Q11303 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\psi_{n}(\beta)}}$ \psi_{n}(\beta)
		Property / Symbols used: Q11303 / qualifier
			xml-id: C5.S20.XMD4.m1dec
		Property / Symbols used
			Q11304
		Property / Symbols used: Q11304 / rank
			Normal rank
		Property / Symbols used: Q11304 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\beta=1/(kT)}}$ \beta=1/(\BoltzmannConstant T)
		Property / Symbols used: Q11304 / qualifier
			xml-id: C5.S20.XMD5.m1dec

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Latest revision as of 01:12, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:5.20.E3	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\psi_{n}(\beta)=\int_{{\mathbb{R}^{n}}}e^{-\beta W}\mathrm{d}x\\ =(2\pi)^{n/2}\beta^{-(n/2)-(\beta n(n-1)/4)}\*\left(\Gamma\left(1+\tfrac{1}{2}\beta\right)\right)^{-n}\prod_{j=1}^{n}\Gamma\left(1+\tfrac{1}{2}j\beta\right).}}$

0 references

DLMF id

DLMF:5.20.E3

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2adec

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

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1adec

0 references

base of natural logarithm

Defining formula

${\displaystyle{\displaystyle\mathrm{e}}}$

xml-id

C4.S2.E11.m2adec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3adec

0 references

Q10812

Defining formula

${\displaystyle{\displaystyle\mathbb{R}}}$

xml-id

introduction.Sx4.p2.t1.r14.m2adec

0 references

Q11292

Defining formula

${\displaystyle{\displaystyle j}}$

xml-id

C5.S1.XMD1.m1adec

0 references

Q11274

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C5.S1.XMD3.m1bdec

0 references

Q11281

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C5.S1.XMD5.m1bdec

0 references

Q11300

Defining formula

${\displaystyle{\displaystyle W}}$

xml-id

C5.S20.XMD1.m1bdec

0 references

Q11303

Defining formula

${\displaystyle{\displaystyle\psi_{n}(\beta)}}$

xml-id

C5.S20.XMD4.m1dec

0 references

Q11304

Defining formula

${\displaystyle{\displaystyle\beta=1/(kT)}}$

xml-id

C5.S20.XMD5.m1dec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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