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DLMF:8.12.E8 - MaRDI portal

DLMF:8.12.E8 (Q3301)

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DLMF:8.12.E8
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    Statements

    DLMF defining formula
    T ⁢ ( a , η ) ∼ e 1 2 ⁢ a ⁢ η 2 2 ⁢ π ⁢ a ⁢ ∑ k = 0 ∞ c k ⁢ ( η ) ⁢ ( - a ) - k , asymptotic-expansion 𝑇 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 T(a,\eta)\sim\frac{e^{\frac{1}{2}a\eta^{2}}}{% \sqrt{2\pi a}}\sum_{k=0}^{\infty}c_{k}(\eta)(-a)^{-k},}}
    0 references
    Symbols used
    Q10905
    DLMF defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11aadec
    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.m2acdec
    0 references
    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
    0 references
    parameter
    DLMF defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1fdec
    0 references
    nonnegative integer
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C8.S1.XMD5.m1adec
    0 references
    η ( λ )
    DLMF defining formula
    η ⁢ ( λ ) 𝜂 𝜆 {\displaystyle{\displaystyle\eta(\lambda)}}
    xml-id
    C8.S12.XMD1.m1gdec
    0 references
    function
    DLMF defining formula
    T ⁢ ( a , η ) 𝑇 𝑎 𝜂 {\displaystyle{\displaystyle T(a,\eta)}}
    xml-id
    C8.S12.XMD4.m1bdec
    0 references
    coefficients
    DLMF defining formula
    c k ⁢ ( η ) subscript 𝑐 𝑘 𝜂 {\displaystyle{\displaystyle c_{k}(\eta)}}
    xml-id
    C8.S12.XMD6.m1adec
    0 references

    Identifiers

     
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