DLMF:36.12.E10 (Q10002): Difference between revisions

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Revision as of 15:20, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 15:20, 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
			Q12755
		Property / Symbols used: Q12755 / rank
			Normal rank
		Property / Symbols used: Q12755 / qualifier
			Defining formula: ${\displaystyle{\displaystyle m}}$ m
		Property / Symbols used: Q12755 / qualifier
			xml-id: C36.S1.XMD3.m1bdec
		Property / Symbols used
			Q12742
		Property / Symbols used: Q12742 / rank
			Normal rank
		Property / Symbols used: Q12742 / qualifier
			Defining formula: ${\displaystyle{\displaystyle t}}$ t
		Property / Symbols used: Q12742 / qualifier
			xml-id: C36.S1.XMD5.m1adec
		Property / Symbols used
			Q12743
		Property / Symbols used: Q12743 / rank
			Normal rank
		Property / Symbols used: Q12743 / qualifier
			Defining formula: ${\displaystyle{\displaystyle K}}$ K
		Property / Symbols used: Q12743 / qualifier
			xml-id: C36.S1.XMD7.m1fdec
		Property / Symbols used
			Q12759
		Property / Symbols used: Q12759 / rank
			Normal rank
		Property / Symbols used: Q12759 / qualifier
			Defining formula: ${\displaystyle{\displaystyle g(u,\mathbf{y})}}$ g(u,\mathbf{y})
		Property / Symbols used: Q12759 / qualifier
			xml-id: C36.S12.XMD2.m1adec
		Property / Symbols used
			Q12760
		Property / Symbols used: Q12760 / rank
			Normal rank
		Property / Symbols used: Q12760 / qualifier
			Defining formula: ${\displaystyle{\displaystyle f(u,\mathbf{y})}}$ f(u,\mathbf{y})
		Property / Symbols used: Q12760 / qualifier
			xml-id: C36.S12.XMD3.m1edec
		Property / Symbols used
			mapping (locally)
		Property / Symbols used: mapping (locally) / rank
			Normal rank
		Property / Symbols used: mapping (locally) / qualifier
			Defining formula: ${\displaystyle{\displaystyle u(t;\mathbf{y})}}$ u(t;\mathbf{y})
		Property / Symbols used: mapping (locally) / qualifier
			xml-id: C36.S12.XMD5.m1edec
		Property / Symbols used
			Q12751
		Property / Symbols used: Q12751 / rank
			Normal rank
		Property / Symbols used: Q12751 / qualifier
			Defining formula: ${\displaystyle{\displaystyle t_{j}(\mathbf{x})}}$ t_{j}(\mathbf{x})
		Property / Symbols used: Q12751 / qualifier
			xml-id: C36.S4.XMD1.m1cdec

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Latest revision as of 15:20, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:36.12.E10	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle G_{n}(\mathbf{y})=g(t_{n}(\mathbf{y}),\mathbf{y})\sqrt{\frac{\ifrac{{\partial}^{2}\Phi_{K}\left(t_{n}(\mathbf{x}(\mathbf{y}));\mathbf{x}(\mathbf{y})\right)}{{\partial t}^{2}}}{\ifrac{{\partial}^{2}f(u_{n}(\mathbf{y}))}{{\partial u}^{2}}}}.}}$

0 references

DLMF id

DLMF:36.12.E10

0 references

Symbols used

cuspoid catastrophe of codimension $$K$$

Defining formula

${\displaystyle{\displaystyle\Phi_{\NVar{K}}\left(\NVar{t};\NVar{\mathbf{x}}\right)}}$

xml-id

C36.S2.E1.m2abdec

0 references

partial derivative of $$f$$ with respect to $$x$$

Defining formula

${\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}$

xml-id

C1.S5.E3.m4abdec

0 references

partial differential of $$x$$

Defining formula

${\displaystyle{\displaystyle\partial\NVar{x}}}$

xml-id

C1.S5.E3.m2abdec

0 references

Q12755

Defining formula

${\displaystyle{\displaystyle m}}$

xml-id

C36.S1.XMD3.m1bdec

0 references

Q12742

Defining formula

${\displaystyle{\displaystyle t}}$

xml-id

C36.S1.XMD5.m1adec

0 references

Q12743

Defining formula

${\displaystyle{\displaystyle K}}$

xml-id

C36.S1.XMD7.m1fdec

0 references

Q12759

Defining formula

${\displaystyle{\displaystyle g(u,\mathbf{y})}}$

xml-id

C36.S12.XMD2.m1adec

0 references

Q12760

Defining formula

${\displaystyle{\displaystyle f(u,\mathbf{y})}}$

xml-id

C36.S12.XMD3.m1edec

0 references

mapping (locally)

Defining formula

${\displaystyle{\displaystyle u(t;\mathbf{y})}}$

xml-id

C36.S12.XMD5.m1edec

0 references

Q12751

Defining formula

${\displaystyle{\displaystyle t_{j}(\mathbf{x})}}$

xml-id

C36.S4.XMD1.m1cdec

0 references

 

Sitelinks

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