DLMF:5.4.E19 (Q2057): Difference between revisions

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Revision as of 11:10, 29 December 2019 Admin (talk | contribs) (‎Created a new Item: Wikidata Toolkit example test item creation)		Latest revision as of 17:30, 1 January 2020 Admin (talk | contribs) (‎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.m2aedec
		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.m2ajdec
		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.m2adec
		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
			psi (or digamma) function
		Property / Symbols used: psi (or digamma) function / rank
			Normal rank
		Property / Symbols used: psi (or digamma) function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}$ \digamma@{\NVar{z}}
		Property / Symbols used: psi (or digamma) function / qualifier
			xml-id: C5.S2.E2.m2agdec
		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
			Q11280
		Property / Symbols used: Q11280 / rank
			Normal rank
		Property / Symbols used: Q11280 / qualifier
			Defining formula: ${\displaystyle{\displaystyle q}}$ q
		Property / Symbols used: Q11280 / qualifier
			xml-id: C5.S1.XMD10.m1dec
		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.m1adec

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Latest revision as of 17:30, 1 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:5.4.E19	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\psi\left(\frac{p}{q}\right)=-\gamma-\ln q-\frac{\pi}{2}\cot\left(\frac{\pi p}{q}\right)+\frac{1}{2}\sum_{k=1}^{q-1}\cos\left(\frac{2\pi kp}{q}\right)\ln\left(2-2\cos\left(\frac{2\pi k}{q}\right)\right).}}$

0 references

DLMF id

DLMF:5.4.E19

0 references

Symbols used

Euler’s constant

Defining formula

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

xml-id

C5.S2.E3.m2aedec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2ajdec

0 references

cosine function

Defining formula

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

xml-id

C4.S14.E2.m2adec

0 references

cotangent function

Defining formula

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

xml-id

C4.S14.E7.m2adec

0 references

psi (or digamma) function

Defining formula

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

xml-id

C5.S2.E2.m2agdec

0 references

principal branch of logarithm function

Defining formula

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

xml-id

C4.S2.E2.m2abdec

0 references

Q11280

Defining formula

${\displaystyle{\displaystyle q}}$

xml-id

C5.S1.XMD10.m1dec

0 references

Q11279

Defining formula

${\displaystyle{\displaystyle k}}$

xml-id

C5.S1.XMD4.m1adec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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