DLMF:25.13.E2 (Q7738): Difference between revisions

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Revision as of 18:18, 30 December 2019 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 13:51, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / constraint
			${\displaystyle{\displaystyle\Re s>1}}$ \Re s>1
		Property / constraint: ${\displaystyle{\displaystyle\Re s>1}}$ / rank
			Normal rank
		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.m2adec
		Property / Symbols used
			Hurwitz zeta function
		Property / Symbols used: Hurwitz zeta function / rank
			Normal rank
		Property / Symbols used: Hurwitz zeta function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}$ \Hurwitzzeta@{\NVar{s}}{\NVar{a}}
		Property / Symbols used: Hurwitz zeta function / qualifier
			xml-id: C25.S11.E1.m2adec
		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.m2aadec
		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.m2aadec
		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.m2aadec
		Property / Symbols used
			periodic zeta function
		Property / Symbols used: periodic zeta function / rank
			Normal rank
		Property / Symbols used: periodic zeta function / qualifier
			Defining formula: ${\displaystyle{\displaystyle F\left(\NVar{x},\NVar{s}\right)}}$ \perZeta@{\NVar{x}}{\NVar{s}}
		Property / Symbols used: periodic zeta function / qualifier
			xml-id: C25.S13.E1.m2aadec
		Property / Symbols used
			Q10811
		Property / Symbols used: Q10811 / rank
			Normal rank
		Property / Symbols used: Q10811 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\Re}}$ \realpart@@
		Property / Symbols used: Q10811 / qualifier
			xml-id: C1.S9.E2.m1adec
		Property / Symbols used
			Q12152
		Property / Symbols used: Q12152 / rank
			Normal rank
		Property / Symbols used: Q12152 / qualifier
			Defining formula: ${\displaystyle{\displaystyle x}}$ x
		Property / Symbols used: Q12152 / qualifier
			xml-id: C25.S1.XMD5.m1adec
		Property / Symbols used
			Q12149
		Property / Symbols used: Q12149 / rank
			Normal rank
		Property / Symbols used: Q12149 / qualifier
			Defining formula: ${\displaystyle{\displaystyle s}}$ s
		Property / Symbols used: Q12149 / qualifier
			xml-id: C25.S1.XMD7.m1adec

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Latest revision as of 13:51, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:25.13.E2	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle F\left(x,s\right)=\frac{\Gamma\left(1-s\right)}{(2\pi)^{1-s}}\*\left(e^{\pi i(1-s)/2}\zeta\left(1-s,x\right)+e^{\pi i(s-1)/2}\zeta\left(1-s,1-x\right)\right),}}$

0 references

DLMF id

DLMF:25.13.E2

0 references

constraint

${\displaystyle{\displaystyle\Re s>1}}$

0 references

${\displaystyle{\displaystyle 0<x<1}}$

0 references

${\displaystyle{\displaystyle\Re s>1}}$

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2adec

0 references

Hurwitz zeta function

Defining formula

${\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}$

xml-id

C25.S11.E1.m2adec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2aadec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2aadec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2aadec

0 references

periodic zeta function

Defining formula

${\displaystyle{\displaystyle F\left(\NVar{x},\NVar{s}\right)}}$

xml-id

C25.S13.E1.m2aadec

0 references

Q10811

Defining formula

${\displaystyle{\displaystyle\Re}}$

xml-id

C1.S9.E2.m1adec

0 references

Q12152

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C25.S1.XMD5.m1adec

0 references

Q12149

Defining formula

${\displaystyle{\displaystyle s}}$

xml-id

C25.S1.XMD7.m1adec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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