DLMF:11.5.E9 (Q3976): Difference between revisions

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Revision as of 14:45, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		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 / 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.m2ahdec
		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.m2aadec
		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.m1ahdec
		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.m2aadec
		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.m3ahdec
		Property / Symbols used
			modified Struve function
		Property / Symbols used: modified Struve function / rank
			Normal rank
		Property / Symbols used: modified Struve function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathbf{L}_{\NVar{\nu}}\left(\NVar{z}\right)}}$ \modStruveL{\NVar{\nu}}@{\NVar{z}}
		Property / Symbols used: modified Struve function / qualifier
			xml-id: C11.S2.E2.m2abdec
		Property / Symbols used
			Q11491
		Property / Symbols used: Q11491 / rank
			Normal rank
		Property / Symbols used: Q11491 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11491 / qualifier
			xml-id: C11.S1.XMD2.m1fdec
		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.m1fdec

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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.E9	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle(\tfrac{1}{2}z)^{-\nu-1}\mathbf{L}_{\nu}\left(z\right)=\frac{1}{2\pi i}\int_{\infty}^{(0+)}\frac{\pi\csc\left(\pi s\right)}{\Gamma\left(\tfrac{3}{2}+s\right)\Gamma\left(\tfrac{3}{2}+\nu+s\right)}(-\tfrac{1}{4}z^{2})^{s}\mathrm{d}s.}}$

0 references

DLMF id

DLMF:11.5.E9

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2afdec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2ahdec

0 references

cosecant function

Defining formula

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

xml-id

C4.S14.E5.m2aadec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1ahdec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2aadec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3ahdec

0 references

modified Struve function

Defining formula

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

xml-id

C11.S2.E2.m2abdec

0 references

Q11491

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C11.S1.XMD2.m1fdec

0 references

Q11492

Defining formula

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

xml-id

C11.S1.XMD3.m1fdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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