DLMF:11.11.E4 (Q4064)

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DLMF:11.11.E4
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    Statements

    Defining formula
    𝐀 Ξ½ ⁑ ( z ) ∼ 1 Ο€ ⁒ z ⁒ βˆ‘ k = 0 ∞ F k ⁒ ( Ξ½ ) z 2 ⁒ k - Ξ½ Ο€ ⁒ z 2 ⁒ βˆ‘ k = 0 ∞ G k ⁒ ( Ξ½ ) z 2 ⁒ k . asymptotic-expansion associated-Anger-Weber-A 𝜈 𝑧 1 πœ‹ 𝑧 superscript subscript π‘˜ 0 subscript 𝐹 π‘˜ 𝜈 superscript 𝑧 2 π‘˜ 𝜈 πœ‹ superscript 𝑧 2 superscript subscript π‘˜ 0 subscript 𝐺 π‘˜ 𝜈 superscript 𝑧 2 π‘˜ {\displaystyle{\displaystyle\mathbf{A}_{\nu}\left(z\right)\sim\frac{1}{\pi z}% \sum_{k=0}^{\infty}\frac{F_{k}(\nu)}{z^{2k}}-\frac{\nu}{\pi z^{2}}\sum_{k=0}^{% \infty}\frac{G_{k}(\nu)}{z^{2k}}.}}
    0 references
    DLMF id
    DLMF:11.11.E4
    0 references
    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.m2adec
    0 references
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11abdec
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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.m2abdec
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    Q11491
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C11.S1.XMD2.m1bdec
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    Q11492
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C11.S1.XMD3.m1cdec
    0 references
    Q11497
    Defining formula
    k π‘˜ {\displaystyle{\displaystyle k}}
    xml-id
    C11.S1.XMD5.m1cdec
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    Q11508
    Defining formula
    F k ⁒ ( Ξ½ ) subscript 𝐹 π‘˜ 𝜈 {\displaystyle{\displaystyle F_{k}(\nu)}}
    xml-id
    C11.S11.XMD1.m1cdec
    0 references
    Q11509
    Defining formula
    G k ⁒ ( Ξ½ ) subscript 𝐺 π‘˜ 𝜈 {\displaystyle{\displaystyle G_{k}(\nu)}}
    xml-id
    C11.S11.XMD2.m1cdec
    0 references
     
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