DLMF:20.10.E4 (Q6840): Difference between revisions

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Revision as of 18:36, 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 14:43, 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
			Q11946
		Property / Symbols used: Q11946 / rank
			Normal rank
		Property / Symbols used: Q11946 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z}\middle|\NVar{\tau}\right)}}$ \Jacobithetatau{\NVar{j}}@{\NVar{z}}{\NVar{\tau}}
		Property / Symbols used: Q11946 / qualifier
			xml-id: C20.S2.SS1.m1acdec
		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.m2acdec
		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.m1acdec
		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
			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.m2adec
		Property / Symbols used
			imaginary unit
		Property / Symbols used: imaginary unit / rank
			Normal rank
		Property / Symbols used: imaginary unit / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{i}}}$ \iunit
		Property / Symbols used: imaginary unit / qualifier
			xml-id: C1.S9.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.m3acdec
		Property / Symbols used
			Q11952
		Property / Symbols used: Q11952 / rank
			Normal rank
		Property / Symbols used: Q11952 / qualifier
			Defining formula: ${\displaystyle{\displaystyle s}}$ s
		Property / Symbols used: Q11952 / qualifier
			xml-id: C20.S10.XMD1.m1dec
		Property / Symbols used
			Q11953
		Property / Symbols used: Q11953 / rank
			Normal rank
		Property / Symbols used: Q11953 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\beta}}$ \beta
		Property / Symbols used: Q11953 / qualifier
			xml-id: C20.S10.XMD2.m1dec
		Property / Symbols used
			Q11954
		Property / Symbols used: Q11954 / rank
			Normal rank
		Property / Symbols used: Q11954 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\ell}}$ \ell
		Property / Symbols used: Q11954 / qualifier
			xml-id: C20.S10.XMD3.m1dec

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Latest revision as of 14:43, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:20.10.E4	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-st}\theta_{1}\left(\frac{\beta\pi}{2\ell}\middle|\frac{i\pi t}{\ell^{2}}\right)\mathrm{d}t=\int_{0}^{\infty}e^{-st}\theta_{2}\left(\frac{(1+\beta)\pi}{2\ell}\middle|\frac{i\pi t}{\ell^{2}}\right)\mathrm{d}t=-\frac{\ell}{\sqrt{s}}\sinh\left(\beta\sqrt{s}\right)\operatorname{sech}\left(\ell\sqrt{s}\right),}}$

0 references

DLMF id

DLMF:20.10.E4

0 references

Symbols used

Q11946

Defining formula

${\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z}\middle|\NVar{\tau}\right)}}$

xml-id

C20.S2.SS1.m1acdec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2acdec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1acdec

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

hyperbolic sine function

Defining formula

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

xml-id

C4.S28.E1.m2adec

0 references

imaginary unit

Defining formula

${\displaystyle{\displaystyle\mathrm{i}}}$

xml-id

C1.S9.E1.m2acdec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3acdec

0 references

Q11952

Defining formula

${\displaystyle{\displaystyle s}}$

xml-id

C20.S10.XMD1.m1dec

0 references

Q11953

Defining formula

${\displaystyle{\displaystyle\beta}}$

xml-id

C20.S10.XMD2.m1dec

0 references

Q11954

Defining formula

${\displaystyle{\displaystyle\ell}}$

xml-id

C20.S10.XMD3.m1dec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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