DLMF:35.5.E5 (Q9798): Difference between revisions

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Revision as of 18:30, 30 December 2019 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 14:52, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / constraint
			${\displaystyle{\displaystyle\mathbf{T}\in{\boldsymbol{\Omega}}}}$ \mathbf{T}\in{\boldsymbol{\Omega}}
		Property / constraint: ${\displaystyle{\displaystyle\mathbf{T}\in{\boldsymbol{\Omega}}}}$ / rank
			Normal rank
		Property / Symbols used
			Q12735
		Property / Symbols used: Q12735 / rank
			Normal rank
		Property / Symbols used: Q12735 / qualifier
			Defining formula: ${\displaystyle{\displaystyle A_{\NVar{\nu}}\left(\NVar{\mathbf{T}}\right)}}$ \BesselAmat{\NVar{\nu}}@{\NVar{\mathbf{T}}}
		Property / Symbols used: Q12735 / qualifier
			xml-id: C35.S5.SS1.m1acdec
		Property / Symbols used
			Q10923
		Property / Symbols used: Q10923 / rank
			Normal rank
		Property / Symbols used: Q10923 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathbb{C}}}$ \Complexes
		Property / Symbols used: Q10923 / qualifier
			xml-id: introduction.Sx4.p1.t1.r1.m2acdec
		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.m1abdec
		Property / Symbols used
			Q10784
		Property / Symbols used: Q10784 / rank
			Normal rank
		Property / Symbols used: Q10784 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\in}}$ \in
		Property / Symbols used: Q10784 / qualifier
			xml-id: introduction.Sx4.p1.t1.r10.m2addec
		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.m3abdec
		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.m1aadec
		Property / Symbols used
			Q12734
		Property / Symbols used: Q12734 / rank
			Normal rank
		Property / Symbols used: Q12734 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathbf{S}}}$ \mathbf{S}
		Property / Symbols used: Q12734 / qualifier
			xml-id: C35.S1.XMD10.m1adec
		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.m1bdec
		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
			Q12727
		Property / Symbols used: Q12727 / rank
			Normal rank
		Property / Symbols used: Q12727 / qualifier
			Defining formula: ${\displaystyle{\displaystyle j}}$ j
		Property / Symbols used: Q12727 / qualifier
			xml-id: C35.S1.XMD4.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.m1ddec
		Property / Symbols used
			Q12733
		Property / Symbols used: Q12733 / rank
			Normal rank
		Property / Symbols used: Q12733 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\boldsymbol{\mathcal{S}}}}$ \boldsymbol{\mathcal{S}}
		Property / Symbols used: Q12733 / qualifier
			xml-id: C35.S1.XMD9.m1bdec

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Latest revision as of 14:52, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:35.5.E5	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\int\limits_{\boldsymbol{{0}}<\mathbf{X}<\mathbf{T}}A_{\nu_{1}}\left(\mathbf{S}_{1}\mathbf{X}\right)|\mathbf{X}|^{\nu_{1}}\*A_{\nu_{2}}\left(\mathbf{S}_{2}(\mathbf{T}-\mathbf{X})\right)|\mathbf{T}-\mathbf{X}|^{\nu_{2}}\mathrm{d}\mathbf{X}=|\mathbf{T}|^{\nu_{1}+\nu_{2}+\frac{1}{2}(m+1)}A_{\nu_{1}+\nu_{2}+\frac{1}{2}(m+1)}\left((\mathbf{S}_{1}+\mathbf{S}_{2})\mathbf{T}\right),}}$

0 references

DLMF id

DLMF:35.5.E5

0 references

constraint

${\displaystyle{\displaystyle\nu_{j}\in\mathbb{C}}}$

0 references

${\displaystyle{\displaystyle\Re(\nu_{j})>-1}}$

0 references

${\displaystyle{\displaystyle j=1,2}}$

0 references

${\displaystyle{\displaystyle\mathbf{S}_{1},\mathbf{S}_{2}\in\boldsymbol{\mathcal{S}}}}$

0 references

${\displaystyle{\displaystyle\mathbf{T}\in{\boldsymbol{\Omega}}}}$

0 references

Symbols used

Q12735

Defining formula

${\displaystyle{\displaystyle A_{\NVar{\nu}}\left(\NVar{\mathbf{T}}\right)}}$

xml-id

C35.S5.SS1.m1acdec

0 references

Q10923

Defining formula

${\displaystyle{\displaystyle\mathbb{C}}}$

xml-id

introduction.Sx4.p1.t1.r1.m2acdec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1abdec

0 references

Q10784

Defining formula

${\displaystyle{\displaystyle\in}}$

xml-id

introduction.Sx4.p1.t1.r10.m2addec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3abdec

0 references

Q10811

Defining formula

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

xml-id

C1.S9.E2.m1aadec

0 references

Q12734

Defining formula

${\displaystyle{\displaystyle\mathbf{S}}}$

xml-id

C35.S1.XMD10.m1adec

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.m1bdec

0 references

Q12720

Defining formula

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

xml-id

C35.S1.XMD13.m1bdec

0 references

Q12727

Defining formula

${\displaystyle{\displaystyle j}}$

xml-id

C35.S1.XMD4.m1dec

0 references

Q12723

Defining formula

${\displaystyle{\displaystyle m}}$

xml-id

C35.S1.XMD8.m1ddec

0 references

Q12733

Defining formula

${\displaystyle{\displaystyle\boldsymbol{\mathcal{S}}}}$

xml-id

C35.S1.XMD9.m1bdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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