DLMF:13.21.E25 (Q4633): 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
			order not exceeding
		Property / Symbols used: order not exceeding / rank
			Normal rank
		Property / Symbols used: order not exceeding / qualifier
			Defining formula: ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$ \bigO@{\NVar{x}}
		Property / Symbols used: order not exceeding / qualifier
			xml-id: C2.S1.E3.m2amdec
		Property / Symbols used
			Whittaker confluent hypergeometric function
		Property / Symbols used: Whittaker confluent hypergeometric function / rank
			Normal rank
		Property / Symbols used: Whittaker confluent hypergeometric function / qualifier
			Defining formula: ${\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}$ \WhittakerconfhyperW{\NVar{\kappa}}{\NVar{\mu}}@{\NVar{z}}
		Property / Symbols used: Whittaker confluent hypergeometric function / qualifier
			xml-id: C13.S14.E3.m2aidec
		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.m2amdec
		Property / Symbols used
			Q11083
		Property / Symbols used: Q11083 / rank
			Normal rank
		Property / Symbols used: Q11083 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{envBi}\left(\NVar{x}\right)}}$ \envAiryBi@{\NVar{x}}
		Property / Symbols used: Q11083 / qualifier
			xml-id: C2.S8.SS3.p4.m6abdec
		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.m2akdec
		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.m2agdec
		Property / Symbols used
			Q11566
		Property / Symbols used: Q11566 / rank
			Normal rank
		Property / Symbols used: Q11566 / qualifier
			Defining formula: ${\displaystyle{\displaystyle x}}$ x
		Property / Symbols used: Q11566 / qualifier
			xml-id: C13.S1.XMD4.m1vdec
		Property / Symbols used
			function (locally)
		Property / Symbols used: function (locally) / rank
			Normal rank
		Property / Symbols used: function (locally) / qualifier
			Defining formula: ${\displaystyle{\displaystyle\widehat{c}(\kappa,\mu)}}$ \widehat{c}(\kappa,\mu)
		Property / Symbols used: function (locally) / qualifier
			xml-id: C13.S21.XMD4.m1cdec
		Property / Symbols used
			function (locally)
		Property / Symbols used: function (locally) / rank
			Normal rank
		Property / Symbols used: function (locally) / qualifier
			Defining formula: ${\displaystyle{\displaystyle\widehat{\Psi}(\kappa,\mu,x)}}$ \widehat{\Psi}(\kappa,\mu,x)
		Property / Symbols used: function (locally) / qualifier
			xml-id: C13.S21.XMD6.m1ddec

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Latest revision as of 15:21, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:13.21.E25	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle W_{-\kappa,\mu}\left(xe^{\pi\mathrm{i}}\right)=e^{-(\kappa-\frac{1}{6})\pi\mathrm{i}}\widehat{c}(\kappa,\mu)\widehat{\Psi}(\kappa,\mu,x)\left(\mathrm{Ai}\left(\kappa^{\frac{2}{3}}\widehat{\zeta}e^{\frac{2}{3}\pi\mathrm{i}}\right)+\mathrm{envBi}\left(\kappa^{\frac{2}{3}}\widehat{\zeta}\right)O\left(\kappa^{-1}\right)\right),}}$

0 references

DLMF id

DLMF:13.21.E25

0 references

Symbols used

Q10919

Defining formula

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

xml-id

C9.S2.SS1.m1acdec

0 references

order not exceeding

Defining formula

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

xml-id

C2.S1.E3.m2amdec

0 references

Whittaker confluent hypergeometric function

Defining formula

${\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}$

xml-id

C13.S14.E3.m2aidec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2amdec

0 references

Q11083

Defining formula

${\displaystyle{\displaystyle\mathrm{envBi}\left(\NVar{x}\right)}}$

xml-id

C2.S8.SS3.p4.m6abdec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2akdec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2agdec

0 references

Q11566

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C13.S1.XMD4.m1vdec

0 references

function (locally)

Defining formula

${\displaystyle{\displaystyle\widehat{c}(\kappa,\mu)}}$

xml-id

C13.S21.XMD4.m1cdec

0 references

function (locally)

Defining formula

${\displaystyle{\displaystyle\widehat{\Psi}(\kappa,\mu,x)}}$

xml-id

C13.S21.XMD6.m1ddec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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