DLMF:35.6.E4 (Q9805): Difference between revisions

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Revision as of 01:02, 30 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 14:54, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / constraint
			${\displaystyle{\displaystyle\Re(a),\Re(b-a)>\frac{1}{2}(m-1)}}$ \realpart@@{(a)},\realpart@@{(b-a)}>\frac{1}{2}(m-1)
		Property / constraint: ${\displaystyle{\displaystyle\Re(a),\Re(b-a)>\frac{1}{2}(m-1)}}$ / rank
			Normal rank
		Property / Symbols used
			generalized hypergeometric function of matrix argument
		Property / Symbols used: generalized hypergeometric function of matrix argument / rank
			Normal rank
		Property / Symbols used: generalized hypergeometric function of matrix argument / qualifier
			Defining formula: ${\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{\mathbf{T}}\right)}}$ \genhyperFmat{\NVar{p}}{\NVar{q}}@{\NVar{a_{1},\dots,a_{p}}}{\NVar{b_{1},\dots,b_{q}}}{\NVar{\mathbf{T}}}
		Property / Symbols used: generalized hypergeometric function of matrix argument / qualifier
			xml-id: C35.S8.E1.m2abdec
		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.m1aadec
		Property / Symbols used
			Q12718
		Property / Symbols used: Q12718 / rank
			Normal rank
		Property / Symbols used: Q12718 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{etr}\left(\NVar{\mathbf{X}}\right)}}$ \exptrace@{\NVar{\mathbf{X}}}
		Property / Symbols used: Q12718 / qualifier
			xml-id: C35.S1.p3.t1.r10.m3aadec
		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.m3aadec
		Property / Symbols used
			multivariate beta function
		Property / Symbols used: multivariate beta function / rank
			Normal rank
		Property / Symbols used: multivariate beta function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{B}_{\NVar{m}}\left(\NVar{a},\NVar{b}\right)}}$ \multivarEulerBeta{\NVar{m}}@{\NVar{a}}{\NVar{b}}
		Property / Symbols used: multivariate beta function / qualifier
			xml-id: C35.S3.E3.m2adec
		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.m1abdec
		Property / Symbols used
			Q12726
		Property / Symbols used: Q12726 / rank
			Normal rank
		Property / Symbols used: Q12726 / qualifier
			Defining formula: ${\displaystyle{\displaystyle a}}$ a
		Property / Symbols used: Q12726 / qualifier
			xml-id: C35.S1.XMD1.m1bdec
		Property / Symbols used
			Q12724
		Property / Symbols used: Q12724 / rank
			Normal rank
		Property / Symbols used: Q12724 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathbf{T}}}$ \mathbf{T}
		Property / Symbols used: Q12724 / qualifier
			xml-id: C35.S1.XMD11.m1cdec
		Property / Symbols used
			Q12719
		Property / Symbols used: Q12719 / rank
			Normal rank
		Property / Symbols used: Q12719 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathbf{X}}}$ \mathbf{X}
		Property / Symbols used: Q12719 / qualifier
			xml-id: C35.S1.XMD12.m1adec
		Property / Symbols used
			Q12728
		Property / Symbols used: Q12728 / rank
			Normal rank
		Property / Symbols used: Q12728 / qualifier
			Defining formula: ${\displaystyle{\displaystyle b}}$ b
		Property / Symbols used: Q12728 / qualifier
			xml-id: C35.S1.XMD2.m1bdec
		Property / Symbols used
			Q12723
		Property / Symbols used: Q12723 / rank
			Normal rank
		Property / Symbols used: Q12723 / qualifier
			Defining formula: ${\displaystyle{\displaystyle m}}$ m
		Property / Symbols used: Q12723 / qualifier
			xml-id: C35.S1.XMD8.m1bdec

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Latest revision as of 14:54, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:35.6.E4	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle{{}_{1}F_{1}}\left({a\atop b};\mathbf{T}\right)=\frac{1}{\mathrm{B}_{m}\left(a,b-a\right)}\int\limits_{\boldsymbol{{0}}<\mathbf{X}<\mathbf{I}}\mathrm{etr}\left(\mathbf{T}\mathbf{X}\right)|\mathbf{X}|^{a-\frac{1}{2}(m+1)}|\mathbf{I}-\mathbf{X}|^{b-a-\frac{1}{2}(m+1)}\mathrm{d}\mathbf{X},}}$

0 references

DLMF id

DLMF:35.6.E4

0 references

constraint

${\displaystyle{\displaystyle\Re(a),\Re(b-a)>\frac{1}{2}(m-1)}}$

0 references

Symbols used

generalized hypergeometric function of matrix argument

Defining formula

${\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{\mathbf{T}}\right)}}$

xml-id

C35.S8.E1.m2abdec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1aadec

0 references

Q12718

Defining formula

${\displaystyle{\displaystyle\mathrm{etr}\left(\NVar{\mathbf{X}}\right)}}$

xml-id

C35.S1.p3.t1.r10.m3aadec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3aadec

0 references

multivariate beta function

Defining formula

${\displaystyle{\displaystyle\mathrm{B}_{\NVar{m}}\left(\NVar{a},\NVar{b}\right)}}$

xml-id

C35.S3.E3.m2adec

0 references

Q10811

Defining formula

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

xml-id

C1.S9.E2.m1abdec

0 references

Q12726

Defining formula

${\displaystyle{\displaystyle a}}$

xml-id

C35.S1.XMD1.m1bdec

0 references

Q12724

Defining formula

${\displaystyle{\displaystyle\mathbf{T}}}$

xml-id

C35.S1.XMD11.m1cdec

0 references

Q12719

Defining formula

${\displaystyle{\displaystyle\mathbf{X}}}$

xml-id

C35.S1.XMD12.m1adec

0 references

Q12728

Defining formula

${\displaystyle{\displaystyle b}}$

xml-id

C35.S1.XMD2.m1bdec

0 references

Q12723

Defining formula

${\displaystyle{\displaystyle m}}$

xml-id

C35.S1.XMD8.m1bdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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