DLMF:19.31.E2 (Q6690): Difference between revisions

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Revision as of 14:24, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 14:24, 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
			Q10765
		Property / Symbols used: Q10765 / rank
			Normal rank
		Property / Symbols used: Q10765 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\det}}$ \det
		Property / Symbols used: Q10765 / qualifier
			xml-id: C1.S3.SS1.m1adec
		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
			exponential function
		Property / Symbols used: exponential function / rank
			Normal rank
		Property / Symbols used: exponential function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\exp\NVar{z}}}$ \exp@@{\NVar{z}}
		Property / Symbols used: exponential function / qualifier
			xml-id: C4.S2.E19.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
			Q11820
		Property / Symbols used: Q11820 / rank
			Normal rank
		Property / Symbols used: Q11820 / qualifier
			Defining formula: ${\displaystyle{\displaystyle n}}$ n
		Property / Symbols used: Q11820 / qualifier
			xml-id: C19.S1.XMD3.m1adec
		Property / Symbols used
			Q11922
		Property / Symbols used: Q11922 / rank
			Normal rank
		Property / Symbols used: Q11922 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\lambda_{n}}}$ \lambda_{n}
		Property / Symbols used: Q11922 / qualifier
			xml-id: C19.S31.XMD1.m1dec

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Latest revision as of 14:24, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:19.31.E2	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\int_{{\mathbb{R}^{n}}}(\mathbf{x}^{\mathrm{T}}\mathbf{A}\mathbf{x})^{\mu}\exp\left(-\mathbf{x}^{\mathrm{T}}\mathbf{B}\mathbf{x}\right)\mathrm{d}x_{1}\cdots\mathrm{d}x_{n}=\frac{\pi^{n/2}\Gamma\left(\mu+\tfrac{1}{2}n\right)}{\sqrt{\det\mathbf{B}}\Gamma\left(\tfrac{1}{2}n\right)}R_{\mu}\left(\tfrac{1}{2},\dots,\tfrac{1}{2};\lambda_{1},\dots,\lambda_{n}\right),}}$

0 references

DLMF id

DLMF:19.31.E2

0 references

constraint

${\displaystyle{\displaystyle\mu>-\tfrac{1}{2}n}}$

0 references

Symbols used

multivariate hypergeometric function

Defining formula

${\displaystyle{\displaystyle R_{\NVar{-a}}\left(\NVar{b_{1}},\dots,\NVar{b_{n}};\NVar{z_{1}},\dots,\NVar{z_{n}}\right)}}$

xml-id

C19.S16.E9.m2adec

0 references

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

Q10765

Defining formula

${\displaystyle{\displaystyle\det}}$

xml-id

C1.S3.SS1.m1adec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1adec

0 references

exponential function

Defining formula

${\displaystyle{\displaystyle\exp\NVar{z}}}$

xml-id

C4.S2.E19.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

Q11820

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C19.S1.XMD3.m1adec

0 references

Q11922

Defining formula

${\displaystyle{\displaystyle\lambda_{n}}}$

xml-id

C19.S31.XMD1.m1dec

0 references

 

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