DLMF:5.17.E7 (Q2187): Difference between revisions

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Revision as of 13:14, 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 01:09, 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
			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.m2aadec
		Property / Symbols used
			Riemann zeta function
		Property / Symbols used: Riemann zeta function / rank
			Normal rank
		Property / Symbols used: Riemann zeta function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}$ \Riemannzeta@{\NVar{s}}
		Property / Symbols used: Riemann zeta function / qualifier
			xml-id: C25.S2.E1.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.m2abdec
		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.m2abdec
		Property / Symbols used
			Q11274
		Property / Symbols used: Q11274 / rank
			Normal rank
		Property / Symbols used: Q11274 / qualifier
			Defining formula: ${\displaystyle{\displaystyle n}}$ n
		Property / Symbols used: Q11274 / qualifier
			xml-id: C5.S1.XMD3.m1adec
		Property / Symbols used
			Q11279
		Property / Symbols used: Q11279 / rank
			Normal rank
		Property / Symbols used: Q11279 / qualifier
			Defining formula: ${\displaystyle{\displaystyle k}}$ k
		Property / Symbols used: Q11279 / qualifier
			xml-id: C5.S1.XMD4.m1bdec
		Property / Symbols used
			Q11297
		Property / Symbols used: Q11297 / rank
			Normal rank
		Property / Symbols used: Q11297 / qualifier
			Defining formula: ${\displaystyle{\displaystyle C}}$ C
		Property / Symbols used: Q11297 / qualifier
			xml-id: C5.S17.XMD2.m1adec

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Latest revision as of 01:09, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:5.17.E7	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle C=\lim_{n\to\infty}\left(\sum_{k=1}^{n}k\ln k-\left(\tfrac{1}{2}n^{2}+\tfrac{1}{2}n+\tfrac{1}{12}\right)\ln n+\tfrac{1}{4}n^{2}\right)=\frac{\gamma+\ln\left(2\pi\right)}{12}-\frac{\zeta'\left(2\right)}{2\pi^{2}}=\frac{1}{12}-\zeta'\left(-1\right),}}$

0 references

DLMF id

DLMF:5.17.E7

0 references

Symbols used

Euler’s constant

Defining formula

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

xml-id

C5.S2.E3.m2aadec

0 references

Riemann zeta function

Defining formula

${\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}$

xml-id

C25.S2.E1.m2adec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2abdec

0 references

principal branch of logarithm function

Defining formula

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

xml-id

C4.S2.E2.m2abdec

0 references

Q11274

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C5.S1.XMD3.m1adec

0 references

Q11279

Defining formula

${\displaystyle{\displaystyle k}}$

xml-id

C5.S1.XMD4.m1bdec

0 references

Q11297

Defining formula

${\displaystyle{\displaystyle C}}$

xml-id

C5.S17.XMD2.m1adec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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