DLMF:9.12.E24 (Q2952): Difference between revisions

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Revision as of 13:40, 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 14:56, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
(7 intermediate revisions by the same user not shown)
		Property / Symbols used
			gamma function
		Property / Symbols used: gamma function / rank
			Normal rank
		Property / Symbols used: gamma function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$ \EulerGamma@{\NVar{z}}
		Property / Symbols used: gamma function / qualifier
			xml-id: C5.S2.E1.m2afdec
		Property / Symbols used
			Scorer function (inhomogeneous Airy function)
		Property / Symbols used: Scorer function (inhomogeneous Airy function) / rank
			Normal rank
		Property / Symbols used: Scorer function (inhomogeneous Airy function) / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{Hi}\left(\NVar{z}\right)}}$ \ScorerHi@{\NVar{z}}
		Property / Symbols used: Scorer function (inhomogeneous Airy function) / qualifier
			xml-id: C9.S12.E5.m2aodec
		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.m2aqdec
		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.m1agdec
		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.m2afdec
		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.m2afdec
		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.m3afdec
		Property / Symbols used
			Q11381
		Property / Symbols used: Q11381 / rank
			Normal rank
		Property / Symbols used: Q11381 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11381 / qualifier
			xml-id: C9.S1.XMD3.m1sdec

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Latest revision as of 14:56, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:9.12.E24	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\mathrm{Hi}\left(z\right)=\frac{3^{-2/3}}{2\pi^{2}i}\int_{-i\infty}^{i\infty}\Gamma\left(\tfrac{1}{3}+\tfrac{1}{3}t\right)\Gamma\left(-t\right)(3^{1/3}e^{\pi i}z)^{t}\mathrm{d}t,}}$

0 references

DLMF id

DLMF:9.12.E24

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2afdec

0 references

Scorer function (inhomogeneous Airy function)

Defining formula

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

xml-id

C9.S12.E5.m2aodec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2aqdec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1agdec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2afdec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2afdec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3afdec

0 references

Q11381

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C9.S1.XMD3.m1sdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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