DLMF:10.22.E17 (Q3391): Difference between revisions

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Revision as of 01:11, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 01:12, 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
			Bessel function of the second kind
		Property / Symbols used: Bessel function of the second kind / rank
			Normal rank
		Property / Symbols used: Bessel function of the second kind / qualifier
			Defining formula: ${\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}$ \BesselY{\NVar{\nu}}@{\NVar{z}}
		Property / Symbols used: Bessel function of the second kind / qualifier
			xml-id: C10.S2.E3.m2adec
		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.m2aedec
		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
			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.m2acdec
		Property / Symbols used
			cotangent function
		Property / Symbols used: cotangent function / rank
			Normal rank
		Property / Symbols used: cotangent function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\cot\NVar{z}}}$ \cot@@{\NVar{z}}
		Property / Symbols used: cotangent function / qualifier
			xml-id: C4.S14.E7.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.m1apdec
		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.m3apdec
		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.m1aedec
		Property / Symbols used
			Q11426
		Property / Symbols used: Q11426 / rank
			Normal rank
		Property / Symbols used: Q11426 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11426 / qualifier
			xml-id: C10.S1.XMD6.m1kdec
		Property / Symbols used
			Q11427
		Property / Symbols used: Q11427 / rank
			Normal rank
		Property / Symbols used: Q11427 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\nu}}$ \nu
		Property / Symbols used: Q11427 / qualifier
			xml-id: C10.S1.XMD7.m1jdec

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Latest revision as of 01:12, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:10.22.E17	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\int_{0}^{\frac{1}{2}\pi}Y_{2\nu}\left(2z\cos\theta\right)\cos\left(2\mu\theta\right)\mathrm{d}\theta=\tfrac{1}{2}\pi\cot\left(2\nu\pi\right)J_{\nu+\mu}\left(z\right)J_{\nu-\mu}\left(z\right)-\tfrac{1}{2}\pi\csc\left(2\nu\pi\right)J_{\mu-\nu}\left(z\right)J_{-\mu-\nu}\left(z\right),}}$

0 references

DLMF id

DLMF:10.22.E17

0 references

constraint

${\displaystyle{\displaystyle-\tfrac{1}{2}<\Re\nu<\tfrac{1}{2}}}$

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.m2aidec

0 references

Bessel function of the second kind

Defining formula

${\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}$

xml-id

C10.S2.E3.m2adec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2aedec

0 references

cosecant function

Defining formula

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

xml-id

C4.S14.E5.m2adec

0 references

cosine function

Defining formula

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

xml-id

C4.S14.E2.m2acdec

0 references

cotangent function

Defining formula

${\displaystyle{\displaystyle\cot\NVar{z}}}$

xml-id

C4.S14.E7.m2adec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1apdec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3apdec

0 references

Q10811

Defining formula

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

xml-id

C1.S9.E2.m1aedec

0 references

Q11426

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C10.S1.XMD6.m1kdec

0 references

Q11427

Defining formula

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

xml-id

C10.S1.XMD7.m1jdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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