DLMF:14.15.E25 (Q4872): Difference between revisions

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Revision as of 01:52, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 01:53, 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
			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.m2agdec
		Property / Symbols used
			Ferrers function of the second kind
		Property / Symbols used: Ferrers function of the second kind / rank
			Normal rank
		Property / Symbols used: Ferrers function of the second kind / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathsf{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}\right)}}$ \FerrersQ[\NVar{\mu}]{\NVar{\nu}}@{\NVar{x}}
		Property / Symbols used: Ferrers function of the second kind / qualifier
			xml-id: C14.S3.E2.m2abdec
		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.m2afdec
		Property / Symbols used
			Q11585
		Property / Symbols used: Q11585 / rank
			Normal rank
		Property / Symbols used: Q11585 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{env}\mskip-1.0mu \overline{U}\left(\NVar{c},\NVar{x}\right)}}$ \envparaUbar@{\NVar{c}}{\NVar{x}}
		Property / Symbols used: Q11585 / qualifier
			xml-id: C14.S15.SS5.p1.m9aadec
		Property / Symbols used
			Q11519
		Property / Symbols used: Q11519 / rank
			Normal rank
		Property / Symbols used: Q11519 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\overline{U}\left(\NVar{a},\NVar{x}\right)}}$ \paraUbar@{\NVar{a}}{\NVar{x}}
		Property / Symbols used: Q11519 / qualifier
			xml-id: C12.S2.SS6.p1.m4aadec
		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.m1pdec
		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.m1rdec
		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.m1rdec
		Property / Symbols used
			Q11620
		Property / Symbols used: Q11620 / rank
			Normal rank
		Property / Symbols used: Q11620 / qualifier
			Defining formula: ${\displaystyle{\displaystyle a}}$ a
		Property / Symbols used: Q11620 / qualifier
			xml-id: C14.S15.XMD13.m1adec
		Property / Symbols used
			Q11621
		Property / Symbols used: Q11621 / rank
			Normal rank
		Property / Symbols used: Q11621 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\zeta}}$ \zeta
		Property / Symbols used: Q11621 / qualifier
			xml-id: C14.S15.XMD14.m1adec
		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.m1hdec

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Latest revision as of 01:53, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:14.15.E25	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\mathsf{Q}^{-\mu}_{\nu}\left(x\right)=\frac{\pi}{\left(\nu+\frac{1}{2}\right)^{1/4}2^{(\nu+\mu+2)/2}\Gamma\left(\frac{1}{2}\nu+\frac{1}{2}\mu+\frac{3}{4}\right)}\*\left(\frac{\zeta^{2}-\alpha^{2}}{x^{2}-a^{2}}\right)^{1/4}\*\left(\overline{U}\left(\mu-\nu-\tfrac{1}{2},\left(2\nu+1\right)^{1/2}\zeta\right)+O\left(\nu^{-2/3}\right)\mathrm{env}\mskip-1.0mu \overline{U}\left(\mu-\nu-\tfrac{1}{2},\left(2\nu+1\right)^{1/2}\zeta\right)\right),}}$

0 references

DLMF id

DLMF:14.15.E25

0 references

Symbols used

order not exceeding

Defining formula

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

xml-id

C2.S1.E3.m2aodec

0 references

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2agdec

0 references

Ferrers function of the second kind

Defining formula

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

xml-id

C14.S3.E2.m2abdec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2afdec

0 references

Q11585

Defining formula

${\displaystyle{\displaystyle\mathrm{env}\mskip-1.0mu \overline{U}\left(\NVar{c},\NVar{x}\right)}}$

xml-id

C14.S15.SS5.p1.m9aadec

0 references

Q11519

Defining formula

${\displaystyle{\displaystyle\overline{U}\left(\NVar{a},\NVar{x}\right)}}$

xml-id

C12.S2.SS6.p1.m4aadec

0 references

Q11589

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C14.S1.XMD1.m1pdec

0 references

Q11591

Defining formula

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

xml-id

C14.S1.XMD7.m1rdec

0 references

Q11590

Defining formula

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

xml-id

C14.S1.XMD8.m1rdec

0 references

Q11620

Defining formula

${\displaystyle{\displaystyle a}}$

xml-id

C14.S15.XMD13.m1adec

0 references

Q11621

Defining formula

${\displaystyle{\displaystyle\zeta}}$

xml-id

C14.S15.XMD14.m1adec

0 references

Q11619

Defining formula

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

xml-id

C14.S15.XMD9.m1hdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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