DLMF:13.21.E2 (Q4610): Difference between revisions

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Revision as of 16:17, 2 January 2020 Admin (talk | contribs) (‎Changed an Item: Add constraint) ← Older edit		Latest revision as of 16:17, 2 January 2020 Admin (talk | contribs) (‎Changed an Item: Add constraint)
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		Property / Symbols used
			Bessel function of the second kind
		Property / Symbols used: Bessel function of the second kind / rank
			Normal rank
		Property / Symbols used: Bessel function of the second kind / qualifier
			Defining formula: ${\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}$ \BesselY{\NVar{\nu}}@{\NVar{z}}
		Property / Symbols used: Bessel function of the second kind / qualifier
			xml-id: C10.S2.E3.m2adec
		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.m2aadec
		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.m2aadec
		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.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.m2adec
		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.m2adec
		Property / Symbols used
			Q11091
		Property / Symbols used: Q11091 / rank
			Normal rank
		Property / Symbols used: Q11091 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{env}\mskip-2.0mu Y_{\NVar{\nu}}\left(\NVar{x}\right)}}$ \envBesselY{\NVar{\nu}}@{\NVar{x}}
		Property / Symbols used: Q11091 / qualifier
			xml-id: C2.S8.SS4.p5.m4adec
		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
			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.m1adec

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Latest revision as of 16:17, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:13.21.E2	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle W_{\kappa,\mu}\left(x\right)=\sqrt{x}\Gamma\left(\kappa+\tfrac{1}{2}\right)\*\left(\sin\left(\kappa\pi-\mu\pi\right)J_{2\mu}\left(2\sqrt{x\kappa}\right)-\cos\left(\kappa\pi-\mu\pi\right)Y_{2\mu}\left(2\sqrt{x\kappa}\right)+\mathrm{env}\mskip-2.0mu Y_{2\mu}\left(2\sqrt{x\kappa}\right)O\left(\kappa^{-\frac{1}{2}}\right)\right),}}$

0 references

DLMF id

DLMF:13.21.E2

0 references

Symbols used

Bessel function of the first kind

Defining formula

${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$

xml-id

C10.S2.E2.m2aadec

0 references

Bessel function of the second kind

Defining formula

${\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}$

xml-id

C10.S2.E3.m2adec

0 references

order not exceeding

Defining formula

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

xml-id

C2.S1.E3.m2aadec

0 references

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2aadec

0 references

Whittaker confluent hypergeometric function

Defining formula

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

xml-id

C13.S14.E3.m2adec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2adec

0 references

cosine function

Defining formula

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

xml-id

C4.S14.E2.m2adec

0 references

Q11091

Defining formula

${\displaystyle{\displaystyle\mathrm{env}\mskip-2.0mu Y_{\NVar{\nu}}\left(\NVar{x}\right)}}$

xml-id

C2.S8.SS4.p5.m4adec

0 references

sine function

Defining formula

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

xml-id

C4.S14.E1.m2adec

0 references

Q11566

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C13.S1.XMD4.m1adec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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