DLMF:25.11.E30 (Q7704): Difference between revisions

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Revision as of 13:43, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 13:43, 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
			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.m1ajdec
		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.m2addec
		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.m2adec
		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.m3ajdec
		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.m1andec
		Property / Symbols used
			Q12161
		Property / Symbols used: Q12161 / rank
			Normal rank
		Property / Symbols used: Q12161 / qualifier
			Defining formula: ${\displaystyle{\displaystyle a}}$ a
		Property / Symbols used: Q12161 / qualifier
			xml-id: C25.S1.XMD6.m1ydec
		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.m1vdec
		Property / Symbols used
			Q12156
		Property / Symbols used: Q12156 / rank
			Normal rank
		Property / Symbols used: Q12156 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q12156 / qualifier
			xml-id: C25.S1.XMD8.m1adec

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Latest revision as of 13:43, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:25.11.E30	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\zeta\left(s,a\right)=\frac{\Gamma\left(1-s\right)}{2\pi i}\int_{-\infty}^{(0+)}\frac{e^{az}z^{s-1}}{1-e^{z}}\mathrm{d}z,}}$

0 references

DLMF id

DLMF:25.11.E30

0 references

constraint

${\displaystyle{\displaystyle\Re a>0}}$

0 references

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

0 references

${\displaystyle{\displaystyle\Re a>0}}$

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2agdec

0 references

Hurwitz zeta function

Defining formula

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

xml-id

C25.S11.E1.m2aaedec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2afdec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1ajdec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2addec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2adec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3ajdec

0 references

Q10811

Defining formula

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

xml-id

C1.S9.E2.m1andec

0 references

Q12161

Defining formula

${\displaystyle{\displaystyle a}}$

xml-id

C25.S1.XMD6.m1ydec

0 references

Q12149

Defining formula

${\displaystyle{\displaystyle s}}$

xml-id

C25.S1.XMD7.m1vdec

0 references

Q12156

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C25.S1.XMD8.m1adec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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