DLMF:8.12.E7 (Q2602)

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DLMF:8.12.E7
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    Statements

    Defining formula
    S ⁢ ( a , η ) ∼ e - 1 2 ⁢ a ⁢ η 2 2 ⁢ π ⁢ a ⁢ ∑ k = 0 ∞ c k ⁢ ( η ) ⁢ a - k , asymptotic-expansion 𝑆 𝑎 𝜂 superscript 𝑒 1 2 𝑎 superscript 𝜂 2 2 𝜋 𝑎 superscript subscript 𝑘 0 subscript 𝑐 𝑘 𝜂 superscript 𝑎 𝑘 {\displaystyle{\displaystyle S(a,\eta)\sim\frac{e^{-\frac{1}{2}a\eta^{2}}}{% \sqrt{2\pi a}}\sum_{k=0}^{\infty}c_{k}(\eta)a^{-k},}}
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    DLMF id
    DLMF:8.12.E7
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    Symbols used
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11adec
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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.m2abdec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
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    Q11324
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1edec
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    Q11330
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C8.S1.XMD5.m1dec
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