DLMF:11.11.E11 (Q4075)

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DLMF:11.11.E11
No description defined

    Statements

    Defining formula
    𝐀 - Ξ½ ⁑ ( Ξ» ⁒ Ξ½ ) ∼ ( 2 Ο€ ⁒ Ξ½ ) 1 / 2 ⁒ e - Ξ½ ⁒ ΞΌ ⁒ βˆ‘ k = 0 ∞ ( 1 2 ) k ⁒ b k ⁒ ( Ξ» ) Ξ½ k , asymptotic-expansion associated-Anger-Weber-A 𝜈 πœ† 𝜈 superscript 2 πœ‹ 𝜈 1 2 superscript 𝑒 𝜈 πœ‡ superscript subscript π‘˜ 0 subscript 1 2 π‘˜ subscript 𝑏 π‘˜ πœ† superscript 𝜈 π‘˜ {\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}},}}
    0 references
    DLMF id
    DLMF:11.11.E11
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    constraint
    Ξ½ β†’ + ∞ β†’ 𝜈 {\displaystyle{\displaystyle\nu\to+\infty}}
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    Symbols used
    Anger–Weber function
    Defining formula
    𝐀 Ξ½ ⁑ ( 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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    Q10931
    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
    Defining formula
    Ο€ {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ahdec
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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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    Q11492
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C11.S1.XMD3.m1hdec
    0 references
    Q11497
    Defining formula
    k π‘˜ {\displaystyle{\displaystyle k}}
    xml-id
    C11.S1.XMD5.m1fdec
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    Q11510
    Defining formula
    Ξ» πœ† {\displaystyle{\displaystyle\lambda}}
    xml-id
    C11.S11.XMD3.m1cdec
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    Q11512
    Defining formula
    b k ⁒ ( Ξ» ) subscript 𝑏 π‘˜ πœ† {\displaystyle{\displaystyle b_{k}(\lambda)}}
    xml-id
    C11.S11.XMD5.m1dec
    0 references
     
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