DLMF:4.40.E7 (Q1979): Difference between revisions

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Revision as of 13:07, 29 December 2019 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Created a new Item: Wikidata Toolkit example test item creation		Latest revision as of 19:22, 1 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / constraint
			${\displaystyle{\displaystyle a\neq 0}}$ a\neq 0
		Property / constraint: ${\displaystyle{\displaystyle a\neq 0}}$ / rank
			Normal rank
		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.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.m2adec
		Property / Symbols used
			hyperbolic cotangent function
		Property / Symbols used: hyperbolic cotangent function / rank
			Normal rank
		Property / Symbols used: hyperbolic cotangent function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\coth\NVar{z}}}$ \coth@@{\NVar{z}}
		Property / Symbols used: hyperbolic cotangent function / qualifier
			xml-id: C4.S28.E7.m2aadec
		Property / Symbols used
			hyperbolic sine function
		Property / Symbols used: hyperbolic sine function / rank
			Normal rank
		Property / Symbols used: hyperbolic sine function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\sinh\NVar{z}}}$ \sinh@@{\NVar{z}}
		Property / Symbols used: hyperbolic sine function / qualifier
			xml-id: C4.S28.E1.m2acdec
		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
			sine function
		Property / Symbols used: sine function / rank
			Normal rank
		Property / Symbols used: sine function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\sin\NVar{z}}}$ \sin@@{\NVar{z}}
		Property / Symbols used: sine function / qualifier
			xml-id: C4.S14.E1.m2adec
		Property / Symbols used
			Q11221
		Property / Symbols used: Q11221 / rank
			Normal rank
		Property / Symbols used: Q11221 / qualifier
			Defining formula: ${\displaystyle{\displaystyle a}}$ a
		Property / Symbols used: Q11221 / qualifier
			xml-id: C4.S1.XMD4.m1dec
		Property / Symbols used
			Q11218
		Property / Symbols used: Q11218 / rank
			Normal rank
		Property / Symbols used: Q11218 / qualifier
			Defining formula: ${\displaystyle{\displaystyle x}}$ x
		Property / Symbols used: Q11218 / qualifier
			xml-id: C4.S1.XMD6.m1fdec

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Latest revision as of 19:22, 1 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:4.40.E7	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-x}\frac{\sin\left(ax\right)}{\sinh x}\mathrm{d}x=\tfrac{1}{2}\pi\coth\left(\tfrac{1}{2}\pi a\right)-\frac{1}{a},}}$

0 references

DLMF id

DLMF:4.40.E7

0 references

constraint

${\displaystyle{\displaystyle a\neq 0}}$

0 references

Symbols used

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.m1afdec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2adec

0 references

hyperbolic cotangent function

Defining formula

${\displaystyle{\displaystyle\coth\NVar{z}}}$

xml-id

C4.S28.E7.m2aadec

0 references

hyperbolic sine function

Defining formula

${\displaystyle{\displaystyle\sinh\NVar{z}}}$

xml-id

C4.S28.E1.m2acdec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3afdec

0 references

sine function

Defining formula

${\displaystyle{\displaystyle\sin\NVar{z}}}$

xml-id

C4.S14.E1.m2adec

0 references

Q11221

Defining formula

${\displaystyle{\displaystyle a}}$

xml-id

C4.S1.XMD4.m1dec

0 references

Q11218

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C4.S1.XMD6.m1fdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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