DLMF:27.12.E5 (Q8089)

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Language	Label	Description	Also known as
English	DLMF:27.12.E5	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\left|\pi\left(x\right)-\mathrm{li}\left(x\right)% \right|=O\left(x\exp\left(-c(\ln x)^{1/2}\right)\right),}}

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DLMF:27.12.E5

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

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order not exceeding

Defining formula

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

C2.S1.E3.m2adec

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exponential function

Defining formula

{\displaystyle{\displaystyle\exp\NVar{z}}}

C4.S2.E19.m2adec

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logarithmic integral

Defining formula

{\displaystyle{\displaystyle\mathrm{li}\left(\NVar{x}\right)}}

C6.S2.E8.m2adec

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principal branch of logarithm function

Defining formula

{\displaystyle{\displaystyle\ln\NVar{z}}}

C4.S2.E2.m2acdec

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number of primes not exceeding $$x$$

Defining formula

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

C27.S2.E2.m2abdec

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Defining formula

{\displaystyle{\displaystyle x}}

C27.S1.XMD6.m1bdec

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