DLMF:24.7.E7 (Q7483): Difference between revisions

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Revision as of 01:34, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 01:34, 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
			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.m2afdec
		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
			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.m1afdec
		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.m2acdec
		Property / Symbols used
			hyperbolic cosine function
		Property / Symbols used: hyperbolic cosine function / rank
			Normal rank
		Property / Symbols used: hyperbolic cosine function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\cosh\NVar{z}}}$ \cosh@@{\NVar{z}}
		Property / Symbols used: hyperbolic cosine function / qualifier
			xml-id: C4.S28.E2.m2adec
		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.m3afdec
		Property / Symbols used
			Q12110
		Property / Symbols used: Q12110 / rank
			Normal rank
		Property / Symbols used: Q12110 / qualifier
			Defining formula: ${\displaystyle{\displaystyle n}}$ n
		Property / Symbols used: Q12110 / qualifier
			xml-id: C24.S1.XMD5.m1fdec
		Property / Symbols used
			Q12111
		Property / Symbols used: Q12111 / rank
			Normal rank
		Property / Symbols used: Q12111 / qualifier
			Defining formula: ${\displaystyle{\displaystyle t}}$ t
		Property / Symbols used: Q12111 / qualifier
			xml-id: C24.S1.XMD6.m1fdec
		Property / Symbols used
			Q12112
		Property / Symbols used: Q12112 / rank
			Normal rank
		Property / Symbols used: Q12112 / qualifier
			Defining formula: ${\displaystyle{\displaystyle x}}$ x
		Property / Symbols used: Q12112 / qualifier
			xml-id: C24.S1.XMD7.m1dec

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Latest revision as of 01:34, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:24.7.E7	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle B_{2n}\left(x\right)=(-1)^{n+1}2n\*\int_{0}^{\infty}\frac{\cos\left(2\pi x\right)-e^{-2\pi t}}{\cosh\left(2\pi t\right)-\cos\left(2\pi x\right)}t^{2n-1}\mathrm{d}t,}}$

0 references

DLMF id

DLMF:24.7.E7

0 references

constraint

${\displaystyle{\displaystyle n=1,2,\dots}}$

0 references

Symbols used

Q11288

Defining formula

${\displaystyle{\displaystyle B_{\NVar{n}}\left(\NVar{x}\right)}}$

xml-id

C24.S2.SS1.m2adec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2afdec

0 references

cosine function

Defining formula

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

xml-id

C4.S14.E2.m2adec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1afdec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2acdec

0 references

hyperbolic cosine function

Defining formula

${\displaystyle{\displaystyle\cosh\NVar{z}}}$

xml-id

C4.S28.E2.m2adec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3afdec

0 references

Q12110

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C24.S1.XMD5.m1fdec

0 references

Q12111

Defining formula

${\displaystyle{\displaystyle t}}$

xml-id

C24.S1.XMD6.m1fdec

0 references

Q12112

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C24.S1.XMD7.m1dec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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