DLMF:12.10.E35 (Q4200): Difference between revisions

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Revision as of 15:18, 29 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 15:21, 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
			Q10919
		Property / Symbols used: Q10919 / rank
			Normal rank
		Property / Symbols used: Q10919 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}$ \AiryAi@{\NVar{z}}
		Property / Symbols used: Q10919 / qualifier
			xml-id: C9.S2.SS1.m1adec
		Property / Symbols used
			Q10931
		Property / Symbols used: Q10931 / rank
			Normal rank
		Property / Symbols used: Q10931 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\sim}}$ \asympexp
		Property / Symbols used: Q10931 / qualifier
			xml-id: C2.S1.SS3.p1.m11andec
		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
			Q11320
		Property / Symbols used: Q11320 / rank
			Normal rank
		Property / Symbols used: Q11320 / qualifier
			Defining formula: ${\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}$ \paraU@{\NVar{a}}{\NVar{z}}
		Property / Symbols used: Q11320 / qualifier
			xml-id: C12.S2.SS1.p1.m1agdec
		Property / Symbols used
			Q11526
		Property / Symbols used: Q11526 / rank
			Normal rank
		Property / Symbols used: Q11526 / qualifier
			Defining formula: ${\displaystyle{\displaystyle s}}$ s
		Property / Symbols used: Q11526 / qualifier
			xml-id: C12.S1.XMD5.m1xdec
		Property / Symbols used
			Q11534
		Property / Symbols used: Q11534 / rank
			Normal rank
		Property / Symbols used: Q11534 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\zeta}}$ \zeta
		Property / Symbols used: Q11534 / qualifier
			xml-id: C12.S10.XMD21.m1dec
		Property / Symbols used
			function (locally)
		Property / Symbols used: function (locally) / rank
			Normal rank
		Property / Symbols used: function (locally) / qualifier
			Defining formula: ${\displaystyle{\displaystyle\phi(\zeta)}}$ \phi(\zeta)
		Property / Symbols used: function (locally) / qualifier
			xml-id: C12.S10.XMD22.m1dec
		Property / Symbols used
			Q11535
		Property / Symbols used: Q11535 / rank
			Normal rank
		Property / Symbols used: Q11535 / qualifier
			Defining formula: ${\displaystyle{\displaystyle A_{s}(\zeta)}}$ A_{s}(\zeta)
		Property / Symbols used: Q11535 / qualifier
			xml-id: C12.S10.XMD23.m1dec
		Property / Symbols used
			Q11536
		Property / Symbols used: Q11536 / rank
			Normal rank
		Property / Symbols used: Q11536 / qualifier
			Defining formula: ${\displaystyle{\displaystyle B_{s}(\zeta)}}$ B_{s}(\zeta)
		Property / Symbols used: Q11536 / qualifier
			xml-id: C12.S10.XMD24.m1dec
		Property / Symbols used
			expansion (locally)
		Property / Symbols used: expansion (locally) / rank
			Normal rank
		Property / Symbols used: expansion (locally) / qualifier
			Defining formula: ${\displaystyle{\displaystyle g(\mu)}}$ g(\mu)
		Property / Symbols used: expansion (locally) / qualifier
			xml-id: C12.S10.XMD7.m1idec

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Latest revision as of 15:21, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:12.10.E35	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle U\left(-\frac{1}{2}\mu^{2},\mu t\sqrt{2}\right)\sim 2\pi^{\frac{1}{2}}\mu^{\frac{1}{3}}g(\mu)\phi(\zeta)\*\left(\mathrm{Ai}\left(\mu^{\frac{4}{3}}\zeta\right)\sum_{s=0}^{\infty}\frac{A_{s}(\zeta)}{\mu^{4s}}+\frac{\mathrm{Ai}'\left(\mu^{\frac{4}{3}}\zeta\right)}{\mu^{\frac{8}{3}}}\sum_{s=0}^{\infty}\frac{B_{s}(\zeta)}{\mu^{4s}}\right),}}$

0 references

DLMF id

DLMF:12.10.E35

0 references

Symbols used

Q10919

Defining formula

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

xml-id

C9.S2.SS1.m1adec

0 references

Q10931

Defining formula

${\displaystyle{\displaystyle\sim}}$

xml-id

C2.S1.SS3.p1.m11andec

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

Q11320

Defining formula

${\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}$

xml-id

C12.S2.SS1.p1.m1agdec

0 references

Q11526

Defining formula

${\displaystyle{\displaystyle s}}$

xml-id

C12.S1.XMD5.m1xdec

0 references

Q11534

Defining formula

${\displaystyle{\displaystyle\zeta}}$

xml-id

C12.S10.XMD21.m1dec

0 references

function (locally)

Defining formula

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

xml-id

C12.S10.XMD22.m1dec

0 references

Q11535

Defining formula

${\displaystyle{\displaystyle A_{s}(\zeta)}}$

xml-id

C12.S10.XMD23.m1dec

0 references

Q11536

Defining formula

${\displaystyle{\displaystyle B_{s}(\zeta)}}$

xml-id

C12.S10.XMD24.m1dec

0 references

expansion (locally)

Defining formula

${\displaystyle{\displaystyle g(\mu)}}$

xml-id

C12.S10.XMD7.m1idec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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