Formula:8361

Digital Library of Mathematical Functions ID 25.9.E1

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

Symbols List

• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: order not exceeding
• ${\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}$: Riemann zeta function
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle s}}$: complex variable
• ${\displaystyle{\displaystyle\sigma}}$: fixed
 

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