DLMF:36.13.E8 (Q10017): Difference between revisions

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Revision as of 15:21, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 15:21, 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
			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.m2abdec
		Property / Symbols used
			Q10777
		Property / Symbols used: Q10777 / rank
			Normal rank
		Property / Symbols used: Q10777 / qualifier
			Defining formula: ${\displaystyle{\displaystyle(\NVar{a},\NVar{b})}}$ (\NVar{a},\NVar{b})
		Property / Symbols used: Q10777 / qualifier
			xml-id: introduction.Sx4.p1.t1.r29.m6aadec
		Property / Symbols used
			sine function
		Property / Symbols used: sine function / rank
			Normal rank
		Property / Symbols used: sine function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\sin\NVar{z}}}$ \sin@@{\NVar{z}}
		Property / Symbols used: sine function / qualifier
			xml-id: C4.S14.E1.m2aadec
		Property / Symbols used
			Q12746
		Property / Symbols used: Q12746 / rank
			Normal rank
		Property / Symbols used: Q12746 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q12746 / qualifier
			xml-id: C36.S1.XMD11.m1adec
		Property / Symbols used
			Q12766
		Property / Symbols used: Q12766 / rank
			Normal rank
		Property / Symbols used: Q12766 / qualifier
			Defining formula: ${\displaystyle{\displaystyle u(\phi)}}$ u(\phi)
		Property / Symbols used: Q12766 / qualifier
			xml-id: C36.S13.XMD4.m1adec
		Property / Symbols used
			Q12767
		Property / Symbols used: Q12767 / rank
			Normal rank
		Property / Symbols used: Q12767 / qualifier
			Defining formula: ${\displaystyle{\displaystyle v(\phi)}}$ v(\phi)
		Property / Symbols used: Q12767 / qualifier
			xml-id: C36.S13.XMD5.m1adec

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Latest revision as of 15:21, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:36.13.E8	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle z(\rho,\phi)=2\pi\left(\rho^{-1/3}u(\phi)\cos\left(\rho\widetilde{f}(\phi)\right)\mathrm{Ai}\left(-\rho^{2/3}\Delta(\phi)\right)\*(1+O\left(1/\rho\right))+\rho^{-2/3}v(\phi)\sin\left(\rho\widetilde{f}(\phi)\right)\mathrm{Ai}'\left(-\rho^{2/3}\Delta(\phi)\right)\*(1+O\left(1/\rho\right))\right),}}$

0 references

DLMF id

DLMF:36.13.E8

0 references

constraint

${\displaystyle{\displaystyle\rho\to\infty}}$

0 references

Symbols used

Q10919

Defining formula

${\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}$

xml-id

C9.S2.SS1.m1adec

0 references

order not exceeding

Defining formula

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

xml-id

C2.S1.E3.m2adec

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.m2abdec

0 references

Q10777

Defining formula

${\displaystyle{\displaystyle(\NVar{a},\NVar{b})}}$

xml-id

introduction.Sx4.p1.t1.r29.m6aadec

0 references

sine function

Defining formula

${\displaystyle{\displaystyle\sin\NVar{z}}}$

xml-id

C4.S14.E1.m2aadec

0 references

Q12746

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C36.S1.XMD11.m1adec

0 references

Q12766

Defining formula

${\displaystyle{\displaystyle u(\phi)}}$

xml-id

C36.S13.XMD4.m1adec

0 references

Q12767

Defining formula

${\displaystyle{\displaystyle v(\phi)}}$

xml-id

C36.S13.XMD5.m1adec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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