DLMF:24.7.E1 (Q7477): Difference between revisions

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Revision as of 01:33, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 01:33, 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
			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.m1adec
		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.m2adec
		Property / Symbols used
			hyperbolic secant function
		Property / Symbols used: hyperbolic secant function / rank
			Normal rank
		Property / Symbols used: hyperbolic secant function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\operatorname{sech}\NVar{z}}}$ \sech@@{\NVar{z}}
		Property / Symbols used: hyperbolic secant function / qualifier
			xml-id: C4.S28.E6.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.m3adec
		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.m1dec
		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.m1dec

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Latest revision as of 01:33, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:24.7.E1	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle B_{2n}=(-1)^{n+1}\frac{4n}{1-2^{1-2n}}\int_{0}^{\infty}\frac{t^{2n-1}}{e^{2\pi t}+1}\mathrm{d}t=(-1)^{n+1}\frac{2n}{1-2^{1-2n}}\int_{0}^{\infty}t^{2n-1}e^{-\pi t}\operatorname{sech}\left(\pi t\right)\mathrm{d}t,}}$

0 references

DLMF id

DLMF:24.7.E1

0 references

Symbols used

Q11109

Defining formula

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

xml-id

C24.S2.SS1.m1adec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2adec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1adec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2adec

0 references

hyperbolic secant function

Defining formula

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

xml-id

C4.S28.E6.m2adec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3adec

0 references

Q12110

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C24.S1.XMD5.m1dec

0 references

Q12111

Defining formula

${\displaystyle{\displaystyle t}}$

xml-id

C24.S1.XMD6.m1dec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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