DLMF:13.21.E22 (Q4630): Difference between revisions

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Revision as of 14:20, 2 January 2020 Admin (talk | contribs) (‎Changed an Item: Add constraint) ← Older edit		Latest revision as of 14:20, 2 January 2020 Admin (talk | contribs) (‎Changed an Item: Add constraint)
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		Property / Symbols used
			cosine function
		Property / Symbols used: cosine function / rank
			Normal rank
		Property / Symbols used: cosine function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\cos\NVar{z}}}$ \cos@@{\NVar{z}}
		Property / Symbols used: cosine function / qualifier
			xml-id: C4.S14.E2.m2abdec
		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.m6adec
		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.m2abdec
		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.m1sdec
		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.m1adec
		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.m1adec

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Latest revision as of 14:20, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:13.21.E22	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle M_{\kappa,\mu}\left(x\right)=\frac{1}{2\pi}\*\Gamma\left(2\mu+1\right)\*\Gamma\left(\kappa-\mu+\tfrac{1}{2}\right)\*\widehat{c}(\kappa,\mu)\*\widehat{\Psi}(\kappa,\mu,x)\*\left(\sin\left(\kappa\pi-\mu\pi\right)\mathrm{Ai}\left(\kappa^{\frac{2}{3}}\widehat{\zeta}\right)+\cos\left(\kappa\pi-\mu\pi\right)\mathrm{Bi}\left(\kappa^{\frac{2}{3}}\widehat{\zeta}\right)+\mathrm{envBi}\left(\kappa^{\frac{2}{3}}\widehat{\zeta}\right)O\left(\kappa^{-1}\right)\right),}}$

0 references

DLMF id

DLMF:13.21.E22

0 references

Symbols used

Q10919

Defining formula

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

xml-id

C9.S2.SS1.m1adec

0 references

Q11081

Defining formula

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

xml-id

C9.S2.SS1.m2adec

0 references

order not exceeding

Defining formula

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

xml-id

C2.S1.E3.m2ajdec

0 references

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2agdec

0 references

Whittaker confluent hypergeometric function

Defining formula

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

xml-id

C13.S14.E2.m2acdec

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

cosine function

Defining formula

${\displaystyle{\displaystyle\cos\NVar{z}}}$

xml-id

C4.S14.E2.m2abdec

0 references

Q11083

Defining formula

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

xml-id

C2.S8.SS3.p4.m6adec

0 references

sine function

Defining formula

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

xml-id

C4.S14.E1.m2abdec

0 references

Q11566

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C13.S1.XMD4.m1sdec

0 references

function (locally)

Defining formula

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

xml-id

C13.S21.XMD4.m1adec

0 references

function (locally)

Defining formula

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

xml-id

C13.S21.XMD6.m1adec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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