DLMF:12.11.E1 (Q4217)

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DLMF:12.11.E1
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    Statements

    Defining formula
    z a , s = e 3 4 ⁢ π ⁢ i ⁢ 2 ⁢ τ s ⁢ ( 1 - i ⁢ a ⁢ λ s 2 ⁢ τ s + 2 ⁢ a 2 ⁢ λ s 2 - 8 ⁢ a 2 ⁢ λ s + 4 ⁢ a 2 + 3 16 ⁢ τ s 2 + O ⁡ ( λ s 3 ⁢ τ s - 3 ) ) , subscript 𝑧 𝑎 𝑠 superscript 𝑒 3 4 𝜋 𝑖 2 subscript 𝜏 𝑠 1 𝑖 𝑎 subscript 𝜆 𝑠 2 subscript 𝜏 𝑠 2 superscript 𝑎 2 superscript subscript 𝜆 𝑠 2 8 superscript 𝑎 2 subscript 𝜆 𝑠 4 superscript 𝑎 2 3 16 superscript subscript 𝜏 𝑠 2 Big-O superscript subscript 𝜆 𝑠 3 superscript subscript 𝜏 𝑠 3 {\displaystyle{\displaystyle z_{a,s}=e^{\frac{3}{4}\pi i}\sqrt{2\tau_{s}}\left% (1-\frac{ia\lambda_{s}}{2\tau_{s}}+\frac{2a^{2}\lambda_{s}^{2}-8a^{2}\lambda_{% s}+4a^{2}+3}{16\tau_{s}^{2}}+O\left(\lambda_{s}^{3}\tau_{s}^{-3}\right)\right)% ,}}
    0 references
    DLMF id
    DLMF:12.11.E1
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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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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
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    Q11513
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C12.S1.XMD3.m1dec
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    Q11526
    Defining formula
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C12.S1.XMD5.m1dec
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    Q11516
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C12.S1.XMD6.m1dec
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    DLMF:12.11.E2
    Defining formula
    τ s subscript 𝜏 𝑠 {\displaystyle{\displaystyle\tau_{s}}}
    xml-id
    C12.S11.XMD1.m1dec
    0 references
     
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