DLMF:25.16.E4 (Q7759)

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DLMF:25.16.E4
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    Statements

    Defining formula
    ψ ⁡ ( x ) = x + O ⁡ ( x 1 2 + ϵ ) , Chebyshev-psi 𝑥 𝑥 Big-O superscript 𝑥 1 2 italic-ϵ {\displaystyle{\displaystyle\psi\left(x\right)=x+O\left(x^{\frac{1}{2}+% \epsilon}\right),}}
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    DLMF id
    DLMF:25.16.E4
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    constraint
    x → ∞ → 𝑥 {\displaystyle{\displaystyle x\to\infty}}
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    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2adec
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    Chebyshev $$\psi$$ -function
    Defining formula
    ψ ⁡ ( x ) Chebyshev-psi 𝑥 {\displaystyle{\displaystyle\psi\left(\NVar{x}\right)}}
    xml-id
    C25.S16.E1.m2acdec
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