DLMF:14.15.E15 (Q4861): Difference between revisions

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Revision as of 01:50, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 01:50, 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
			Q11090
		Property / Symbols used: Q11090 / rank
			Normal rank
		Property / Symbols used: Q11090 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{env}\mskip-2.0mu J_{\NVar{\nu}}\left(\NVar{x}\right)}}$ \envBesselJ{\NVar{\nu}}@{\NVar{x}}
		Property / Symbols used: Q11090 / qualifier
			xml-id: C2.S8.SS4.p5.m2aadec
		Property / Symbols used
			Q11589
		Property / Symbols used: Q11589 / rank
			Normal rank
		Property / Symbols used: Q11589 / qualifier
			Defining formula: ${\displaystyle{\displaystyle x}}$ x
		Property / Symbols used: Q11589 / qualifier
			xml-id: C14.S1.XMD1.m1hdec
		Property / Symbols used
			Q11591
		Property / Symbols used: Q11591 / rank
			Normal rank
		Property / Symbols used: Q11591 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mu}}$ \mu
		Property / Symbols used: Q11591 / qualifier
			xml-id: C14.S1.XMD7.m1kdec
		Property / Symbols used
			Q11590
		Property / Symbols used: Q11590 / rank
			Normal rank
		Property / Symbols used: Q11590 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\nu}}$ \nu
		Property / Symbols used: Q11590 / qualifier
			xml-id: C14.S1.XMD8.m1kdec
		Property / Symbols used
			Q11617
		Property / Symbols used: Q11617 / rank
			Normal rank
		Property / Symbols used: Q11617 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\beta}}$ \beta
		Property / Symbols used: Q11617 / qualifier
			xml-id: C14.S15.XMD10.m1dec
		Property / Symbols used
			Q11618
		Property / Symbols used: Q11618 / rank
			Normal rank
		Property / Symbols used: Q11618 / qualifier
			Defining formula: ${\displaystyle{\displaystyle y}}$ y
		Property / Symbols used: Q11618 / qualifier
			xml-id: C14.S15.XMD11.m1dec
		Property / Symbols used
			Q11619
		Property / Symbols used: Q11619 / rank
			Normal rank
		Property / Symbols used: Q11619 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\alpha}}$ \alpha
		Property / Symbols used: Q11619 / qualifier
			xml-id: C14.S15.XMD9.m1dec

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Latest revision as of 01:50, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:14.15.E15	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\mathsf{P}^{-\mu}_{\nu}\left(x\right)=\beta\left(\frac{y-\alpha^{2}}{1-\alpha^{2}-x^{2}}\right)^{1/4}\*\left(J_{\mu}\left(\left(\nu+\tfrac{1}{2}\right)y^{1/2}\right)+O\left(\frac{1}{\nu}\right)\mathrm{env}\mskip-2.0mu J_{\mu}\left(\left(\nu+\tfrac{1}{2}\right)y^{1/2}\right)\right),}}$

0 references

DLMF id

DLMF:14.15.E15

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

order not exceeding

Defining formula

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

xml-id

C2.S1.E3.m2ajdec

0 references

Ferrers function of the first kind

Defining formula

${\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}\right)}}$

xml-id

C14.S3.E1.m2acdec

0 references

Q11090

Defining formula

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

xml-id

C2.S8.SS4.p5.m2aadec

0 references

Q11589

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C14.S1.XMD1.m1hdec

0 references

Q11591

Defining formula

${\displaystyle{\displaystyle\mu}}$

xml-id

C14.S1.XMD7.m1kdec

0 references

Q11590

Defining formula

${\displaystyle{\displaystyle\nu}}$

xml-id

C14.S1.XMD8.m1kdec

0 references

Q11617

Defining formula

${\displaystyle{\displaystyle\beta}}$

xml-id

C14.S15.XMD10.m1dec

0 references

Q11618

Defining formula

${\displaystyle{\displaystyle y}}$

xml-id

C14.S15.XMD11.m1dec

0 references

Q11619

Defining formula

${\displaystyle{\displaystyle\alpha}}$

xml-id

C14.S15.XMD9.m1dec

0 references

 

Sitelinks

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