DLMF:11.11.E4 (Q4064): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10931 / rank
 
Normal rank
Property / Symbols used: Q10931 / qualifier
 
Defining formula:

∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}

\asympexp
Property / Symbols used: Q10931 / qualifier
 
xml-id: C2.S1.SS3.p1.m11abdec

Revision as of 15:00, 2 January 2020

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DLMF:11.11.E4
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    Statements

    Defining formula
    𝐀 ν ⁡ ( z ) ∼ 1 π ⁢ z ⁢ ∑ k = 0 ∞ F k ⁢ ( ν ) z 2 ⁢ k - ν π ⁢ z 2 ⁢ ∑ k = 0 ∞ G k ⁢ ( ν ) z 2 ⁢ k . asymptotic-expansion associated-Anger-Weber-A 𝜈 𝑧 1 𝜋 𝑧 superscript subscript 𝑘 0 subscript 𝐹 𝑘 𝜈 superscript 𝑧 2 𝑘 𝜈 𝜋 superscript 𝑧 2 superscript subscript 𝑘 0 subscript 𝐺 𝑘 𝜈 superscript 𝑧 2 𝑘 {\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 ν ⁡ ( 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
    0 references
     
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