DLMF:36.11.E4 (Q9987): Difference between revisions

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Revision as of 01:08, 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 15:17, 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
			canonical integral function
		Property / Symbols used: canonical integral function / rank
			Normal rank
		Property / Symbols used: canonical integral function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\Psi_{\NVar{K}}\left(\NVar{\mathbf{x}}\right)}}$ \canonint{\NVar{K}}@{\NVar{\mathbf{x}}}
		Property / Symbols used: canonical integral function / qualifier
			xml-id: C36.S2.E4.m2abdec
		Property / Symbols used
			the ratio of the circumference of a circle to its diameter
		Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
			Normal rank
		Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
			Defining formula: ${\displaystyle{\displaystyle\pi}}$ \cpi
		Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
			xml-id: C3.S12.E1.m2abdec
		Property / Symbols used
			cosine function
		Property / Symbols used: cosine function / rank
			Normal rank
		Property / Symbols used: cosine function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\cos\NVar{z}}}$ \cos@@{\NVar{z}}
		Property / Symbols used: cosine function / qualifier
			xml-id: C4.S14.E2.m2adec
		Property / Symbols used
			exponential function
		Property / Symbols used: exponential function / rank
			Normal rank
		Property / Symbols used: exponential function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\exp\NVar{z}}}$ \exp@@{\NVar{z}}
		Property / Symbols used: exponential function / qualifier
			xml-id: C4.S2.E19.m2abdec
		Property / Symbols used
			order less than
		Property / Symbols used: order less than / rank
			Normal rank
		Property / Symbols used: order less than / qualifier
			Defining formula: ${\displaystyle{\displaystyle o\left(\NVar{x}\right)}}$ \littleo@{\NVar{x}}
		Property / Symbols used: order less than / qualifier
			xml-id: C2.S1.E2.m2abdec
		Property / Symbols used
			Q12748
		Property / Symbols used: Q12748 / rank
			Normal rank
		Property / Symbols used: Q12748 / qualifier
			Defining formula: ${\displaystyle{\displaystyle x}}$ x
		Property / Symbols used: Q12748 / qualifier
			xml-id: C36.S1.XMD9.m1dec

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Latest revision as of 15:17, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:36.11.E4	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\Psi_{3}\left(x,0,0\right)=\frac{\sqrt{2\pi}}{(5|x|^{3})^{1/8}}\begin{cases}\exp\left(-2\sqrt{2}(\ifrac{x}{5})^{5/4}\right)\left(\cos\left(2\sqrt{2}(\ifrac{x}{5})^{5/4}-\tfrac{1}{8}\pi\right)+o\left(1\right)\right),&x\to+\infty,\\ \cos\left(4(\ifrac{|x|}{5})^{5/4}-\tfrac{1}{4}\pi\right)+o\left(1\right),&x\to-\infty.\end{cases}}}$

0 references

DLMF id

DLMF:36.11.E4

0 references

Symbols used

canonical integral function

Defining formula

${\displaystyle{\displaystyle\Psi_{\NVar{K}}\left(\NVar{\mathbf{x}}\right)}}$

xml-id

C36.S2.E4.m2abdec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

${\displaystyle{\displaystyle\pi}}$

xml-id

C3.S12.E1.m2abdec

0 references

cosine function

Defining formula

${\displaystyle{\displaystyle\cos\NVar{z}}}$

xml-id

C4.S14.E2.m2adec

0 references

exponential function

Defining formula

${\displaystyle{\displaystyle\exp\NVar{z}}}$

xml-id

C4.S2.E19.m2abdec

0 references

order less than

Defining formula

${\displaystyle{\displaystyle o\left(\NVar{x}\right)}}$

xml-id

C2.S1.E2.m2abdec

0 references

Q12748

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C36.S1.XMD9.m1dec

0 references

 

Sitelinks

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