DLMF:11.5.E8 (Q3975): Difference between revisions

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Revision as of 15:11, 29 December 2019 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Created a new Item: Wikidata Toolkit example test item creation		Latest revision as of 14:45, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / constraint
			${\displaystyle{\displaystyle\Re\nu>-1}}$ \realpart@@{\nu}>-1
		Property / constraint: ${\displaystyle{\displaystyle\Re\nu>-1}}$ / rank
			Normal rank
		Property / constraint
			${\displaystyle{\displaystyle x>0}}$ x>0
		Property / constraint: ${\displaystyle{\displaystyle x>0}}$ / rank
			Normal rank
		Property / constraint
			${\displaystyle{\displaystyle\Re\nu>-1}}$ \Re\nu>-1
		Property / constraint: ${\displaystyle{\displaystyle\Re\nu>-1}}$ / rank
			Normal rank
		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.m2aedec
		Property / Symbols used
			Struve function
		Property / Symbols used: Struve function / rank
			Normal rank
		Property / Symbols used: Struve function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathbf{H}_{\NVar{\nu}}\left(\NVar{z}\right)}}$ \StruveH{\NVar{\nu}}@{\NVar{z}}
		Property / Symbols used: Struve function / qualifier
			xml-id: C11.S2.E1.m2aadec
		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.m2agdec
		Property / Symbols used
			cosecant function
		Property / Symbols used: cosecant function / rank
			Normal rank
		Property / Symbols used: cosecant function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\csc\NVar{z}}}$ \csc@@{\NVar{z}}
		Property / Symbols used: cosecant function / qualifier
			xml-id: C4.S14.E5.m2adec
		Property / Symbols used
			Q10770
		Property / Symbols used: Q10770 / rank
			Normal rank
		Property / Symbols used: Q10770 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$ \diff{\NVar{x}}
		Property / Symbols used: Q10770 / qualifier
			xml-id: C1.S4.SS4.m1agdec
		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.m2adec
		Property / Symbols used
			Q10771
		Property / Symbols used: Q10771 / rank
			Normal rank
		Property / Symbols used: Q10771 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\int}}$ \int
		Property / Symbols used: Q10771 / qualifier
			xml-id: C1.S4.SS4.m3agdec
		Property / Symbols used
			Q10811
		Property / Symbols used: Q10811 / rank
			Normal rank
		Property / Symbols used: Q10811 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\Re}}$ \realpart@@
		Property / Symbols used: Q10811 / qualifier
			xml-id: C1.S9.E2.m1afdec
		Property / Symbols used
			Q11494
		Property / Symbols used: Q11494 / rank
			Normal rank
		Property / Symbols used: Q11494 / qualifier
			Defining formula: ${\displaystyle{\displaystyle x}}$ x
		Property / Symbols used: Q11494 / qualifier
			xml-id: C11.S1.XMD1.m1adec
		Property / Symbols used
			Q11492
		Property / Symbols used: Q11492 / rank
			Normal rank
		Property / Symbols used: Q11492 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\nu}}$ \nu
		Property / Symbols used: Q11492 / qualifier
			xml-id: C11.S1.XMD3.m1edec

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Latest revision as of 14:45, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:11.5.E8	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle(\tfrac{1}{2}x)^{-\nu-1}\mathbf{H}_{\nu}\left(x\right)=-\frac{1}{2\pi i}\int_{-i\infty}^{i\infty}\frac{\pi\csc\left(\pi s\right)}{\Gamma\left(\tfrac{3}{2}+s\right)\Gamma\left(\tfrac{3}{2}+\nu+s\right)}(\tfrac{1}{4}x^{2})^{s}\mathrm{d}s,}}$

0 references

DLMF id

DLMF:11.5.E8

0 references

constraint

${\displaystyle{\displaystyle\Re\nu>-1}}$

0 references

${\displaystyle{\displaystyle x>0}}$

0 references

${\displaystyle{\displaystyle\Re\nu>-1}}$

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2aedec

0 references

Struve function

Defining formula

${\displaystyle{\displaystyle\mathbf{H}_{\NVar{\nu}}\left(\NVar{z}\right)}}$

xml-id

C11.S2.E1.m2aadec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2agdec

0 references

cosecant function

Defining formula

${\displaystyle{\displaystyle\csc\NVar{z}}}$

xml-id

C4.S14.E5.m2adec

0 references

Q10770

Defining formula

${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$

xml-id

C1.S4.SS4.m1agdec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2adec

0 references

Q10771

Defining formula

${\displaystyle{\displaystyle\int}}$

xml-id

C1.S4.SS4.m3agdec

0 references

Q10811

Defining formula

${\displaystyle{\displaystyle\Re}}$

xml-id

C1.S9.E2.m1afdec

0 references

Q11494

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C11.S1.XMD1.m1adec

0 references

Q11492

Defining formula

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

xml-id

C11.S1.XMD3.m1edec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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