Formula:8724

Digital Library of Mathematical Functions ID 27.5.E7

${\displaystyle{\displaystyle G(x)=\sum_{m=1}^{\infty}\frac{F(mx)}{m^{s}}\Longleftrightarrow F(x)=\sum_{m=1}^{\infty}\mu\left(m\right)\frac{G(mx)}{m^{s}},}}$

Symbols List

• ${\displaystyle{\displaystyle\mu\left(\NVar{n}\right)}}$: Möbius function
• ${\displaystyle{\displaystyle m}}$: positive integer
• ${\displaystyle{\displaystyle x}}$: real number
• ${\displaystyle{\displaystyle F(s)}}$: Dirichlet series
• ${\displaystyle{\displaystyle G(s)}}$: Dirichlet series
 

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