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DLMF:26.3.E12 - MaRDI portal

DLMF:26.3.E12 (Q8478)

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DLMF:26.3.E12
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    Statements

    DLMF defining formula
    ( 2 ⁢ n n ) ∼ 4 n π ⁢ n , asymptotically-equals binomial 2 𝑛 𝑛 superscript 4 𝑛 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{2n}{n}\sim\frac{4^{n}}{% \sqrt{\pi n}},}}
    0 references
    constraint
    n → ∞ → 𝑛 {\displaystyle{\displaystyle n\to\infty}}
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    Symbols used
    asymptotic equality
    DLMF defining formula
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2adec
    0 references
    Q10728
    DLMF defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1amdec
    0 references
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C26.S1.XMD6.m1mdec
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    Identifiers

     
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