Formula:DLMF:25.16:E3

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${\displaystyle{\displaystyle{\displaystyle\psi\left(x\right)=x+o\left(x\right)}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle x\to\infty}}}$

Note(s)

The prime number theorem is equivalent to this statement

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\psi}}}$ : Chebyshev ${\displaystyle{\displaystyle{\displaystyle\psi}}}$-function : http://dlmf.nist.gov/25.16#E1
${\displaystyle{\displaystyle{\displaystyle o}}}$ : order less than : http://dlmf.nist.gov/2.1#E2

Bibliography

Equation (3), Section 25.16 of DLMF.

URL links

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