DLMF:25.5.E13 (Q7626): Difference between revisions

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Revision as of 18:14, 30 December 2019 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 13:27, 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.m2ahdec
		Property / Symbols used
			Riemann zeta function
		Property / Symbols used: Riemann zeta function / rank
			Normal rank
		Property / Symbols used: Riemann zeta function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}$ \Riemannzeta@{\NVar{s}}
		Property / Symbols used: Riemann zeta function / qualifier
			xml-id: C25.S2.E1.m2aldec
		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.m1aldec
		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.m3aldec
		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.m1ldec
		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.m1ldec

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Latest revision as of 13:27, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:25.5.E13	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\zeta\left(s\right)=\frac{\pi^{s/2}}{s(s-1)\Gamma\left(\frac{1}{2}s\right)}+\frac{\pi^{s/2}}{\Gamma\left(\frac{1}{2}s\right)}\*\int_{1}^{\infty}\left(x^{s/2}+x^{(1-s)/2}\right)\frac{\omega(x)}{x}\mathrm{d}x,}}$

0 references

DLMF id

DLMF:25.5.E13

0 references

constraint

${\displaystyle{\displaystyle s\neq 1}}$

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2ahdec

0 references

Riemann zeta function

Defining formula

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

xml-id

C25.S2.E1.m2aldec

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.m1aldec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3aldec

0 references

Q12152

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C25.S1.XMD5.m1ldec

0 references

Q12149

Defining formula

${\displaystyle{\displaystyle s}}$

xml-id

C25.S1.XMD7.m1ldec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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