DLMF:11.11.E10 (Q4074): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
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.m11addec

Revision as of 15:01, 2 January 2020

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DLMF:11.11.E10
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    Statements

    Defining formula
    𝐀 - ν ⁡ ( λ ⁢ ν ) ∼ - 1 π ⁢ ∑ k = 0 ∞ ( 2 ⁢ k ) ! ⁢ a k ⁢ ( - λ ) ν 2 ⁢ k + 1 , asymptotic-expansion associated-Anger-Weber-A 𝜈 𝜆 𝜈 1 𝜋 superscript subscript 𝑘 0 2 𝑘 subscript 𝑎 𝑘 𝜆 superscript 𝜈 2 𝑘 1 {\displaystyle{\displaystyle\mathbf{A}_{-\nu}\left(\lambda\nu\right)\sim-\frac% {1}{\pi}\sum_{k=0}^{\infty}\frac{(2k)!\,a_{k}(-\lambda)}{\nu^{2k+1}},}}
    0 references
    DLMF id
    DLMF:11.11.E10
    0 references
    constraint
    ν → + ∞ → 𝜈 {\displaystyle{\displaystyle\nu\to+\infty}}
    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.m2abdec
    0 references
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11addec
    0 references
     
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