DLMF:10.8.E2 (Q3064): Difference between revisions

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Revision as of 13:43, 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 15:10, 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 first kind
		Property / Symbols used: Bessel function of the first kind / rank
			Normal rank
		Property / Symbols used: Bessel function of the first kind / qualifier
			Defining formula: ${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$ \BesselJ{\NVar{\nu}}@{\NVar{z}}
		Property / Symbols used: Bessel function of the first kind / qualifier
			xml-id: C10.S2.E2.m2aadec
		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.m2aadec
		Property / Symbols used
			Euler’s constant
		Property / Symbols used: Euler’s constant / rank
			Normal rank
		Property / Symbols used: Euler’s constant / qualifier
			Defining formula: ${\displaystyle{\displaystyle\gamma}}$ \EulerConstant
		Property / Symbols used: Euler’s constant / qualifier
			xml-id: C5.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.m2aadec
		Property / Symbols used
			Q10755
		Property / Symbols used: Q10755 / rank
			Normal rank
		Property / Symbols used: Q10755 / qualifier
			Defining formula: ${\displaystyle{\displaystyle!}}$ !
		Property / Symbols used: Q10755 / qualifier
			xml-id: introduction.Sx4.p1.t1.r15.m5aadec
		Property / Symbols used
			principal branch of logarithm function
		Property / Symbols used: principal branch of logarithm function / rank
			Normal rank
		Property / Symbols used: principal branch of logarithm function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\ln\NVar{z}}}$ \ln@@{\NVar{z}}
		Property / Symbols used: principal branch of logarithm function / qualifier
			xml-id: C4.S2.E2.m2aadec
		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.m1adec

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Latest revision as of 15:10, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:10.8.E2	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle Y_{0}\left(z\right)=\frac{2}{\pi}\left(\ln\left(\tfrac{1}{2}z\right)+\gamma\right)J_{0}\left(z\right)+\frac{2}{\pi}\left(\frac{\tfrac{1}{4}z^{2}}{(1!)^{2}}-(1+\tfrac{1}{2})\frac{(\tfrac{1}{4}z^{2})^{2}}{(2!)^{2}}+(1+\tfrac{1}{2}+\tfrac{1}{3})\frac{(\tfrac{1}{4}z^{2})^{3}}{(3!)^{2}}-\cdots\right),}}$

0 references

DLMF id

DLMF:10.8.E2

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.m2aadec

0 references

Bessel function of the second kind

Defining formula

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

xml-id

C10.S2.E3.m2aadec

0 references

Euler’s constant

Defining formula

${\displaystyle{\displaystyle\gamma}}$

xml-id

C5.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.m2aadec

0 references

Q10755

Defining formula

${\displaystyle{\displaystyle!}}$

xml-id

introduction.Sx4.p1.t1.r15.m5aadec

0 references

principal branch of logarithm function

Defining formula

${\displaystyle{\displaystyle\ln\NVar{z}}}$

xml-id

C4.S2.E2.m2aadec

0 references

Q11426

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C10.S1.XMD6.m1adec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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