DLMF:13.9.E10 (Q4453)

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DLMF:13.9.E10
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    Statements

    Defining formula
    a = - π 2 4 ⁢ z ⁢ ( n 2 + ( b - 3 2 ) ⁢ n ) - 1 16 ⁢ z ⁢ ( ( b - 3 2 ) 2 ⁢ π 2 + 4 3 ⁢ z 2 - 8 ⁢ b ⁢ ( z - 1 ) - 4 ⁢ b 2 - 3 ) + O ⁡ ( n - 1 ) , 𝑎 superscript 𝜋 2 4 𝑧 superscript 𝑛 2 𝑏 3 2 𝑛 1 16 𝑧 superscript 𝑏 3 2 2 superscript 𝜋 2 4 3 superscript 𝑧 2 8 𝑏 𝑧 1 4 superscript 𝑏 2 3 Big-O superscript 𝑛 1 {\displaystyle{\displaystyle a=-\frac{\pi^{2}}{4z}\left(n^{2}+(b-\tfrac{3}{2})% n\right)-\frac{1}{16z}\left((b-\tfrac{3}{2})^{2}\pi^{2}+\tfrac{4}{3}z^{2}-8b(z% -1)-4b^{2}-3\right)+O\left(n^{-1}\right),}}
    0 references
    DLMF id
    DLMF:13.9.E10
    0 references
    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2abdec
    0 references
    Q11559
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C13.S1.XMD2.m1adec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    Q11557
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1adec
    0 references
     
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