DLMF:11.10.E31 (Q4053): Difference between revisions

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Revision as of 14:59, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 14:59, 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.m2axdec
		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.m2amdec
		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.m2andec
		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.m1abdec
		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.m1zdec
		Property / Symbols used
			Q11497
		Property / Symbols used: Q11497 / rank
			Normal rank
		Property / Symbols used: Q11497 / qualifier
			Defining formula: ${\displaystyle{\displaystyle k}}$ k
		Property / Symbols used: Q11497 / qualifier
			xml-id: C11.S1.XMD5.m1edec

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Latest revision as of 14:59, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:11.10.E31	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle{\mathbf{E}_{\nu}\left(z\right)=}\\ {-2\cos\left(\tfrac{1}{2}\nu\pi\right)\sum_{k=0}^{\infty}(-1)^{k}J_{k-\frac{1}{2}\nu+\frac{1}{2}}\left(\tfrac{1}{2}z\right)J_{k+\frac{1}{2}\nu+\frac{1}{2}}\left(\tfrac{1}{2}z\right)}+{2\sin\left(\tfrac{1}{2}\nu\pi\right)\sideset{}{{}^{\prime}}{\sum}_{k=0}^{\infty}(-1)^{k}J_{k-\frac{1}{2}\nu}\left(\tfrac{1}{2}z\right)J_{k+\frac{1}{2}\nu}\left(\tfrac{1}{2}z\right)},}}$

0 references

DLMF id

DLMF:11.10.E31

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.m2addec

0 references

Weber function

Defining formula

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

xml-id

C11.S10.E2.m2ardec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2axdec

0 references

cosine function

Defining formula

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

xml-id

C4.S14.E2.m2amdec

0 references

sine function

Defining formula

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

xml-id

C4.S14.E1.m2andec

0 references

Q11491

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C11.S1.XMD2.m1abdec

0 references

Q11492

Defining formula

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

xml-id

C11.S1.XMD3.m1zdec

0 references

Q11497

Defining formula

${\displaystyle{\displaystyle k}}$

xml-id

C11.S1.XMD5.m1edec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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