DLMF:25.9.E1 (Q7668)

From DRMF

Jump to navigation Jump to search

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:25.9.E1

0 references

order not exceeding

Defining formula

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

C2.S1.E3.m2adec

0 references

Riemann zeta function

Defining formula

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

C25.S2.E1.m2adec

0 references

Defining formula

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

C1.S9.E1.m2adec

0 references

Defining formula

{\displaystyle{\displaystyle n}}

C25.S1.XMD3.m1dec

0 references

Defining formula

{\displaystyle{\displaystyle x}}

C25.S1.XMD5.m1dec

0 references

Defining formula

{\displaystyle{\displaystyle s}}

C25.S1.XMD7.m1dec

0 references

Defining formula

{\displaystyle{\displaystyle\sigma}}

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"