DLMF:8.19.E18 (Q2704): Difference between revisions

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Revision as of 17:12, 30 December 2019 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 14:11, 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
			gamma function
		Property / Symbols used: gamma function / rank
			Normal rank
		Property / Symbols used: gamma function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$ \EulerGamma@{\NVar{z}}
		Property / Symbols used: gamma function / qualifier
			xml-id: C5.S2.E1.m2addec
		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
			Q10784
		Property / Symbols used: Q10784 / rank
			Normal rank
		Property / Symbols used: Q10784 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\in}}$ \in
		Property / Symbols used: Q10784 / qualifier
			xml-id: introduction.Sx4.p1.t1.r10.m2adec
		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.m2aldec
		Property / Symbols used
			generalized exponential integral
		Property / Symbols used: generalized exponential integral / rank
			Normal rank
		Property / Symbols used: generalized exponential integral / qualifier
			Defining formula: ${\displaystyle{\displaystyle E_{\NVar{p}}\left(\NVar{z}\right)}}$ \genexpintE{\NVar{p}}@{\NVar{z}}
		Property / Symbols used: generalized exponential integral / qualifier
			xml-id: C8.S19.E1.m2avdec
		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.m2addec
		Property / Symbols used
			Q10818
		Property / Symbols used: Q10818 / rank
			Normal rank
		Property / Symbols used: Q10818 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathbb{Z}}}$ \Integers
		Property / Symbols used: Q10818 / qualifier
			xml-id: introduction.Sx4.p2.t1.r20.m2adec
		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
			Q11323
		Property / Symbols used: Q11323 / rank
			Normal rank
		Property / Symbols used: Q11323 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11323 / qualifier
			xml-id: C8.S1.XMD2.m1pdec
		Property / Symbols used
			Q11377
		Property / Symbols used: Q11377 / rank
			Normal rank
		Property / Symbols used: Q11377 / qualifier
			Defining formula: ${\displaystyle{\displaystyle p}}$ p
		Property / Symbols used: Q11377 / qualifier
			xml-id: C8.S1.XMD4.m1ndec

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Latest revision as of 14:11, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:8.19.E18	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle E_{p}\left(ze^{2m\pi i}\right)=\frac{2\pi ie^{mp\pi i}}{\Gamma\left(p\right)}\frac{\sin\left(mp\pi\right)}{\sin\left(p\pi\right)}z^{p-1}+E_{p}\left(z\right),}}$

0 references

DLMF id

DLMF:8.19.E18

0 references

constraint

${\displaystyle{\displaystyle m\in\mathbb{Z}}}$

0 references

${\displaystyle{\displaystyle m\in\mathbb{Z}}}$

0 references

${\displaystyle{\displaystyle z\neq 0}}$

0 references

Symbols used

gamma function

Defining formula

${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$

xml-id

C5.S2.E1.m2addec

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

Q10784

Defining formula

${\displaystyle{\displaystyle\in}}$

xml-id

introduction.Sx4.p1.t1.r10.m2adec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2aldec

0 references

generalized exponential integral

Defining formula

${\displaystyle{\displaystyle E_{\NVar{p}}\left(\NVar{z}\right)}}$

xml-id

C8.S19.E1.m2avdec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2addec

0 references

Q10818

Defining formula

${\displaystyle{\displaystyle\mathbb{Z}}}$

xml-id

introduction.Sx4.p2.t1.r20.m2adec

0 references

sine function

Defining formula

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

xml-id

C4.S14.E1.m2adec

0 references

Q11323

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C8.S1.XMD2.m1pdec

0 references

Q11377

Defining formula

${\displaystyle{\displaystyle p}}$

xml-id

C8.S1.XMD4.m1ndec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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