DLMF:5.9.E10 (Q2099): Difference between revisions

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Revision as of 19:37, 1 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 19:37, 1 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		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
			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.m1aidec
		Property / Symbols used
			base of natural logarithm
		Property / Symbols used: base of natural logarithm / rank
			Normal rank
		Property / Symbols used: base of natural logarithm / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{e}}}$ \expe
		Property / Symbols used: base of natural logarithm / qualifier
			xml-id: C4.S2.E11.m2addec
		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.m3aidec
		Property / Symbols used
			Q10816
		Property / Symbols used: Q10816 / rank
			Normal rank
		Property / Symbols used: Q10816 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}$ \atan@@{\NVar{z}}
		Property / Symbols used: Q10816 / qualifier
			xml-id: C4.S23.SS2.p1.m7adec
		Property / Symbols used
			general logarithm function
		Property / Symbols used: general logarithm function / rank
			Normal rank
		Property / Symbols used: general logarithm function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\operatorname{Ln}\NVar{z}}}$ \Ln@@{\NVar{z}}
		Property / Symbols used: general logarithm function / qualifier
			xml-id: C4.S2.E1.m2adec
		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
			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.m1gdec

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Latest revision as of 19:37, 1 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:5.9.E10	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\operatorname{Ln}\Gamma\left(z\right)=\left(z-\tfrac{1}{2}\right)\ln z-z+\tfrac{1}{2}\ln\left(2\pi\right)+2\int_{0}^{\infty}\frac{\operatorname{arctan}\left(t/z\right)}{e^{2\pi t}-1}\mathrm{d}t,}}$

0 references

DLMF id

DLMF:5.9.E10

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2aidec

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

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1aidec

0 references

base of natural logarithm

Defining formula

${\displaystyle{\displaystyle\mathrm{e}}}$

xml-id

C4.S2.E11.m2addec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3aidec

0 references

Q10816

Defining formula

${\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}$

xml-id

C4.S23.SS2.p1.m7adec

0 references

general logarithm function

Defining formula

${\displaystyle{\displaystyle\operatorname{Ln}\NVar{z}}}$

xml-id

C4.S2.E1.m2adec

0 references

principal branch of logarithm function

Defining formula

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

xml-id

C4.S2.E2.m2adec

0 references

Q11273

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C5.S1.XMD7.m1gdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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