DLMF:9.5.E3 (Q2775): Difference between revisions

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Revision as of 13:34, 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 14:24, 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
			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.m2adec
		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
			Q11243
		Property / Symbols used: Q11243 / rank
			Normal rank
		Property / Symbols used: Q11243 / qualifier
			Defining formula: ${\displaystyle{\displaystyle[\NVar{a},\NVar{b})}}$ [\NVar{a},\NVar{b})
		Property / Symbols used: Q11243 / qualifier
			xml-id: introduction.Sx4.p2.t1.r1.m4adec
		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.m1abdec
		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.m2adec
		Property / Symbols used
			base of natural logarithm
		Property / Symbols used: base of natural logarithm / rank
			Normal rank
		Property / Symbols used: base of natural logarithm / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{e}}}$ \expe
		Property / Symbols used: base of natural logarithm / qualifier
			xml-id: C4.S2.E11.m2adec
		Property / Symbols used
			imaginary unit
		Property / Symbols used: imaginary unit / rank
			Normal rank
		Property / Symbols used: imaginary unit / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{i}}}$ \iunit
		Property / Symbols used: imaginary unit / qualifier
			xml-id: C1.S9.E1.m2adec
		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.m3abdec
		Property / Symbols used
			Q11244
		Property / Symbols used: Q11244 / rank
			Normal rank
		Property / Symbols used: Q11244 / qualifier
			Defining formula: ${\displaystyle{\displaystyle(\NVar{a},\NVar{b}]}}$ (\NVar{a},\NVar{b}]
		Property / Symbols used: Q11244 / qualifier
			xml-id: introduction.Sx4.p2.t1.r1.m3adec
		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.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.m1bdec

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Latest revision as of 14:24, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:9.5.E3	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\mathrm{Bi}\left(x\right)=\frac{1}{\pi}\int_{0}^{\infty}\exp\left(-{\tfrac{1}{3}}t^{3}+xt\right)\mathrm{d}t+\frac{1}{\pi}\int_{0}^{\infty}\sin\left(\tfrac{1}{3}t^{3}+xt\right)\mathrm{d}t.}}$

0 references

DLMF id

DLMF:9.5.E3

0 references

Symbols used

Q11081

Defining formula

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

xml-id

C9.S2.SS1.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

Q11243

Defining formula

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

xml-id

introduction.Sx4.p2.t1.r1.m4adec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1abdec

0 references

exponential function

Defining formula

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

xml-id

C4.S2.E19.m2adec

0 references

base of natural logarithm

Defining formula

${\displaystyle{\displaystyle\mathrm{e}}}$

xml-id

C4.S2.E11.m2adec

0 references

imaginary unit

Defining formula

${\displaystyle{\displaystyle\mathrm{i}}}$

xml-id

C1.S9.E1.m2adec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3abdec

0 references

Q11244

Defining formula

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

xml-id

introduction.Sx4.p2.t1.r1.m3adec

0 references

sine function

Defining formula

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

xml-id

C4.S14.E1.m2adec

0 references

Q11382

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C9.S1.XMD2.m1bdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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