DLMF:35.7.E5 (Q9816): Difference between revisions

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Revision as of 14:57, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 14:58, 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
			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.m1dec
		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.m1cdec
		Property / Symbols used
			Q12736
		Property / Symbols used: Q12736 / rank
			Normal rank
		Property / Symbols used: Q12736 / qualifier
			Defining formula: ${\displaystyle{\displaystyle c}}$ c
		Property / Symbols used: Q12736 / qualifier
			xml-id: C35.S1.XMD3.m1cdec
		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.m1cdec

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Latest revision as of 14:58, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:35.7.E5	No description defined

Statements

Defining formula

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

0 references

DLMF id

DLMF:35.7.E5

0 references

constraint

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

0 references

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

0 references

${\displaystyle{\displaystyle\boldsymbol{{0}}<\mathbf{T}<\mathbf{I}}}$

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.m2addec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1adec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3adec

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.m1aadec

0 references

Q12726

Defining formula

${\displaystyle{\displaystyle a}}$

xml-id

C35.S1.XMD1.m1cdec

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.m1dec

0 references

Q12728

Defining formula

${\displaystyle{\displaystyle b}}$

xml-id

C35.S1.XMD2.m1cdec

0 references

Q12736

Defining formula

${\displaystyle{\displaystyle c}}$

xml-id

C35.S1.XMD3.m1cdec

0 references

Q12723

Defining formula

${\displaystyle{\displaystyle m}}$

xml-id

C35.S1.XMD8.m1cdec

0 references

 

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