DLMF:4.19.E8 (Q1687): Difference between revisions

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Revision as of 17:00, 30 December 2019 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 18:22, 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
			Q11109
		Property / Symbols used: Q11109 / rank
			Normal rank
		Property / Symbols used: Q11109 / qualifier
			Defining formula: ${\displaystyle{\displaystyle B_{\NVar{n}}}}$ \BernoullinumberB{\NVar{n}}
		Property / Symbols used: Q11109 / qualifier
			xml-id: C24.S2.SS1.m1addec
		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
			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.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.m5agdec
		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
			Q11223
		Property / Symbols used: Q11223 / rank
			Normal rank
		Property / Symbols used: Q11223 / qualifier
			Defining formula: ${\displaystyle{\displaystyle n}}$ n
		Property / Symbols used: Q11223 / qualifier
			xml-id: C4.S1.XMD3.m1edec
		Property / Symbols used
			Q11217
		Property / Symbols used: Q11217 / rank
			Normal rank
		Property / Symbols used: Q11217 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11217 / qualifier
			xml-id: C4.S1.XMD8.m1gdec

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Latest revision as of 18:22, 1 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:4.19.E8	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\ln\left(\cos z\right)=\sum_{n=1}^{\infty}\frac{(-1)^{n}2^{2n-1}(2^{2n}-1)B_{2n}}{n(2n)!}z^{2n},}}$

0 references

DLMF id

DLMF:4.19.E8

0 references

constraint

${\displaystyle{\displaystyle|z|<\frac{1}{2}\pi}}$

0 references

Symbols used

Q11109

Defining formula

${\displaystyle{\displaystyle B_{\NVar{n}}}}$

xml-id

C24.S2.SS1.m1addec

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

cosine function

Defining formula

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

xml-id

C4.S14.E2.m2aadec

0 references

Q10755

Defining formula

${\displaystyle{\displaystyle!}}$

xml-id

introduction.Sx4.p1.t1.r15.m5agdec

0 references

principal branch of logarithm function

Defining formula

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

xml-id

C4.S2.E2.m2aadec

0 references

Q11223

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C4.S1.XMD3.m1edec

0 references

Q11217

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C4.S1.XMD8.m1gdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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