Difference between revisions of "DLMF:5.7.E3 (Q2079)"

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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 17:33, 1 January 2020 Admin (talk | contribs) (‎Changed an Item: Add constraint)
(6 intermediate revisions by the same user not shown)
		Property / constraint
		+	${\displaystyle{\displaystyle|z|<2}}$ |z|<2
		Property / constraint: ${\displaystyle{\displaystyle|z|<2}}$ / rank
		+	Normal rank
		Property / Symbols used
		+	gamma function
		Property / Symbols used: gamma function / rank
		+	Normal rank
		Property / Symbols used: gamma function / qualifier
		+	Defining formula: ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$ \EulerGamma@{\NVar{z}}
		Property / Symbols used: gamma function / qualifier
		+	xml-id: C5.S2.E1.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.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.m2aadec
		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.m2adec
		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
		+	Q11273
		Property / Symbols used: Q11273 / rank
		+	Normal rank
		Property / Symbols used: Q11273 / qualifier
		+	Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11273 / qualifier
		+	xml-id: C5.S1.XMD7.m1adec

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Latest revision as of 17:33, 1 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:5.7.E3	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\ln\Gamma\left(1+z\right)=-\ln\left(1+z\right)+z(1-\gamma)+\sum_{k=2}^{\infty}(-1)^{k}(\zeta\left(k\right)-1)\frac{z^{k}}{k},}}$

0 references

DLMF id

DLMF:5.7.E3

0 references

constraint

${\displaystyle{\displaystyle|z|<2}}$

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2aadec

0 references

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.m2aadec

0 references

principal branch of logarithm function

Defining formula

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

xml-id

C4.S2.E2.m2adec

0 references

Q11279

Defining formula

${\displaystyle{\displaystyle k}}$

xml-id

C5.S1.XMD4.m1bdec

0 references

Q11273

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C5.S1.XMD7.m1adec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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