DLMF:35.6.E8 (Q9809): Difference between revisions

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Revision as of 14:56, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 14:56, 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
			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.m1gdec
		Property / Symbols used
			Q12720
		Property / Symbols used: Q12720 / rank
			Normal rank
		Property / Symbols used: Q12720 / qualifier
			Defining formula: ${\displaystyle{\displaystyle{\boldsymbol{\Omega}}}}$ {\boldsymbol{\Omega}}
		Property / Symbols used: Q12720 / qualifier
			xml-id: C35.S1.XMD13.m1bdec
		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.m1fdec
		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.m1dec
		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.m1edec

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Latest revision as of 14:56, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:35.6.E8	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\int_{\boldsymbol{\Omega}}|\mathbf{T}|^{c-\frac{1}{2}(m+1)}\Psi\left(a;b;\mathbf{T}\right)\mathrm{d}\mathbf{T}=\frac{\Gamma_{m}\left(c\right)\Gamma_{m}\left(a-c\right)\Gamma_{m}\left(c-b+\frac{1}{2}(m+1)\right)}{\Gamma_{m}\left(a\right)\Gamma_{m}\left(a-b+\frac{1}{2}(m+1)\right)},}}$

0 references

DLMF id

DLMF:35.6.E8

0 references

constraint

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

0 references

${\displaystyle{\displaystyle\Re(c-b)>-1}}$

0 references

Symbols used

confluent hypergeometric function of matrix argument (second kind)

Defining formula

${\displaystyle{\displaystyle\Psi\left(\NVar{a};\NVar{b};\NVar{\mathbf{T}}\right)}}$

xml-id

C35.S6.E2.m2aadec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1addec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3addec

0 references

Q12725

Defining formula

${\displaystyle{\displaystyle\Gamma_{\NVar{m}}\left(\NVar{a}\right)}}$

xml-id

C35.S3.SS1.m1acdec

0 references

Q10811

Defining formula

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

xml-id

C1.S9.E2.m1aedec

0 references

Q12726

Defining formula

${\displaystyle{\displaystyle a}}$

xml-id

C35.S1.XMD1.m1fdec

0 references

Q12724

Defining formula

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

xml-id

C35.S1.XMD11.m1gdec

0 references

Q12720

Defining formula

${\displaystyle{\displaystyle{\boldsymbol{\Omega}}}}$

xml-id

C35.S1.XMD13.m1bdec

0 references

Q12728

Defining formula

${\displaystyle{\displaystyle b}}$

xml-id

C35.S1.XMD2.m1fdec

0 references

Q12736

Defining formula

${\displaystyle{\displaystyle c}}$

xml-id

C35.S1.XMD3.m1dec

0 references

Q12723

Defining formula

${\displaystyle{\displaystyle m}}$

xml-id

C35.S1.XMD8.m1edec

0 references

 

Sitelinks

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