DLMF:11.11.E11 (Q4772): Difference between revisions

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DLMF:11.11.E11
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    Statements

    DLMF defining formula
    𝐀 - ν ⁡ ( λ ⁢ ν ) ∼ ( 2 π ⁢ ν ) 1 / 2 ⁢ e - ν ⁢ μ ⁢ ∑ k = 0 ∞ ( 1 2 ) k ⁢ b k ⁢ ( λ ) ν k , asymptotic-expansion associated-Anger-Weber-A 𝜈 𝜆 𝜈 superscript 2 𝜋 𝜈 1 2 superscript 𝑒 𝜈 𝜇 superscript subscript 𝑘 0 subscript 1 2 𝑘 subscript 𝑏 𝑘 𝜆 superscript 𝜈 𝑘 {\displaystyle{\displaystyle\mathbf{A}_{-\nu}\left(\lambda\nu\right)\sim\left(% \frac{2}{\pi\nu}\right)^{1/2}e^{-\nu\mu}\sum_{k=0}^{\infty}\frac{(\tfrac{1}{2}% )_{k}b_{k}(\lambda)}{\nu^{k}},}}
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    constraint
    ν → + ∞ → 𝜈 {\displaystyle{\displaystyle\nu\to+\infty}}
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    Symbols used
    Anger–Weber function
    DLMF defining formula
    𝐀 ν ⁡ ( z ) associated-Anger-Weber-A 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{A}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S10.E4.m2acdec
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    Q10905
    DLMF defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11aedec
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    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ahdec
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    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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    real or complex order
    DLMF defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C11.S1.XMD3.m1hdec
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    nonnegative integer
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C11.S1.XMD5.m1fdec
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    parameter
    DLMF defining formula
    λ 𝜆 {\displaystyle{\displaystyle\lambda}}
    xml-id
    C11.S11.XMD3.m1cdec
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    expansion function
    DLMF defining formula
    b k ⁢ ( λ ) subscript 𝑏 𝑘 𝜆 {\displaystyle{\displaystyle b_{k}(\lambda)}}
    xml-id
    C11.S11.XMD5.m1dec
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    Identifiers

     
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