DLMF:9.11.E19 (Q2926): Difference between revisions

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Revision as of 13:39, 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 14:51, 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.m1ajdec
		Property / Symbols used
			Q11081
		Property / Symbols used: Q11081 / rank
			Normal rank
		Property / Symbols used: Q11081 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}$ \AiryBi@{\NVar{z}}
		Property / Symbols used: Q11081 / qualifier
			xml-id: C9.S2.SS1.m2afdec
		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.m2ajdec
		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.m1apdec
		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.m3apdec
		Property / Symbols used
			Airy modulus function
		Property / Symbols used: Airy modulus function / rank
			Normal rank
		Property / Symbols used: Airy modulus function / qualifier
			Defining formula: ${\displaystyle{\displaystyle M\left(\NVar{z}\right)}}$ \AirymodM@{\NVar{z}}
		Property / Symbols used: Airy modulus function / qualifier
			xml-id: C9.S8.E3.m2adec
		Property / Symbols used
			Airy modulus function
		Property / Symbols used: Airy modulus function / rank
			Normal rank
		Property / Symbols used: Airy modulus function / qualifier
			Defining formula: ${\displaystyle{\displaystyle N\left(\NVar{z}\right)}}$ \AirymodderivN@{\NVar{z}}
		Property / Symbols used: Airy modulus function / qualifier
			xml-id: C9.S8.E7.m2adec
		Property / Symbols used
			Airy phase function
		Property / Symbols used: Airy phase function / rank
			Normal rank
		Property / Symbols used: Airy phase function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\phi\left(\NVar{z}\right)}}$ \Airyphasederivphi@{\NVar{z}}
		Property / Symbols used: Airy phase function / qualifier
			xml-id: C9.S8.E8.m2adec
		Property / Symbols used
			Airy phase function
		Property / Symbols used: Airy phase function / rank
			Normal rank
		Property / Symbols used: Airy phase function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\theta\left(\NVar{z}\right)}}$ \Airyphasetheta@{\NVar{z}}
		Property / Symbols used: Airy phase function / qualifier
			xml-id: C9.S8.E4.m2adec
		Property / Symbols used
			Q11382
		Property / Symbols used: Q11382 / rank
			Normal rank
		Property / Symbols used: Q11382 / qualifier
			Defining formula: ${\displaystyle{\displaystyle x}}$ x
		Property / Symbols used: Q11382 / qualifier
			xml-id: C9.S1.XMD2.m1adec

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Latest revision as of 14:51, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:9.11.E19	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\int_{0}^{\infty}\frac{\mathrm{d}t}{{\mathrm{Ai}^{2}}\left(t\right)+{\mathrm{Bi}^{2}}\left(t\right)}=\int_{0}^{\infty}\frac{t\mathrm{d}t}{{\mathrm{Ai}'^{2}}\left(t\right)+{\mathrm{Bi}'^{2}}\left(t\right)}=\frac{\pi^{2}}{6}.}}$

0 references

DLMF id

DLMF:9.11.E19

0 references

Symbols used

Q10919

Defining formula

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

xml-id

C9.S2.SS1.m1ajdec

0 references

Q11081

Defining formula

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

xml-id

C9.S2.SS1.m2afdec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2ajdec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1apdec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3apdec

0 references

Airy modulus function

Defining formula

${\displaystyle{\displaystyle M\left(\NVar{z}\right)}}$

xml-id

C9.S8.E3.m2adec

0 references

Airy modulus function

Defining formula

${\displaystyle{\displaystyle N\left(\NVar{z}\right)}}$

xml-id

C9.S8.E7.m2adec

0 references

Airy phase function

Defining formula

${\displaystyle{\displaystyle\phi\left(\NVar{z}\right)}}$

xml-id

C9.S8.E8.m2adec

0 references

Airy phase function

Defining formula

${\displaystyle{\displaystyle\theta\left(\NVar{z}\right)}}$

xml-id

C9.S8.E4.m2adec

0 references

Q11382

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C9.S1.XMD2.m1adec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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