DLMF:25.9.E1 (Q7668): Difference between revisions

From DRMF

Jump to navigation Jump to search

← Older edit

Revision as of 13:34, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 13:34, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
(5 intermediate revisions by the same user not shown)
		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.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.m2adec
		Property / Symbols used
			Q12148
		Property / Symbols used: Q12148 / rank
			Normal rank
		Property / Symbols used: Q12148 / qualifier
			Defining formula: ${\displaystyle{\displaystyle n}}$ n
		Property / Symbols used: Q12148 / qualifier
			xml-id: C25.S1.XMD3.m1dec
		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.m1dec
		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.m1dec
		Property / Symbols used
			Q12157
		Property / Symbols used: Q12157 / rank
			Normal rank
		Property / Symbols used: Q12157 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\sigma}}$ \sigma
		Property / Symbols used: Q12157 / qualifier
			xml-id: C25.S9.XMD1.m1dec

---

Latest revision as of 13:34, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:25.9.E1	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\zeta\left(\sigma+it\right)=\sum_{1\leq n\leq x}\frac{1}{n^{s}}+\chi(s)\sum_{1\leq n\leq y}\frac{1}{n^{1-s}}+O\left(x^{-\sigma}\right)+O\left(y^{\sigma-1}t^{\frac{1}{2}-\sigma}\right),}}$

0 references

DLMF id

DLMF:25.9.E1

0 references

Symbols used

order not exceeding

Defining formula

${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$

xml-id

C2.S1.E3.m2adec

0 references

Riemann zeta function

Defining formula

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

xml-id

C25.S2.E1.m2adec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2adec

0 references

Q12148

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C25.S1.XMD3.m1dec

0 references

Q12152

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C25.S1.XMD5.m1dec

0 references

Q12149

Defining formula

${\displaystyle{\displaystyle s}}$

xml-id

C25.S1.XMD7.m1dec

0 references

Q12157

Defining formula

${\displaystyle{\displaystyle\sigma}}$

xml-id

C25.S9.XMD1.m1dec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q7668&oldid=37841"