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DLMF:36.7.E8 - MaRDI portal

DLMF:36.7.E8 (Q10634)

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DLMF:36.7.E8
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    Statements

    DLMF defining formula
    r = 3 ⁢ ( ( 2 ⁢ n - 1 ) ⁢ π 4 ⁢ | sin ⁡ ( 3 2 ⁢ θ ) | ) 2 / 3 ⁢ ( 1 + O ⁡ ( n - 1 ) ) , 𝑟 3 superscript 2 𝑛 1 𝜋 4 3 2 𝜃 2 3 1 Big-O superscript 𝑛 1 {\displaystyle{\displaystyle r=3\left(\frac{(2n-1)\pi}{4|\sin\left(\tfrac{3}{2% }\theta\right)|}\right)^{2/3}(1+O\left(n^{-1}\right)),}}
    0 references
    constraint
    n → ∞ → 𝑛 {\displaystyle{\displaystyle n\to\infty}}
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    Symbols used
    order not exceeding
    DLMF defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2adec
    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.m2afdec
    0 references
    sine function
    DLMF defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2adec
    0 references
    integer
    DLMF defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C36.S1.XMD3.m1gdec
    0 references
     
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