DLMF:11.11.E8 (Q4069): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2afdec

Revision as of 15:01, 2 January 2020

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DLMF:11.11.E8
No description defined

    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}},}}
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    DLMF id
    DLMF:11.11.E8
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    constraint
    | ph ⁡ ν | ≤ π - δ phase 𝜈 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}\nu|\leq\pi-\delta}}
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    | ph ⁡ ν | ≤ π - δ ph 𝜈 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}\nu|\leq\pi-\delta}}
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    < π absent 𝜋 {\displaystyle{\displaystyle<\pi}}
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    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.m2aadec
    0 references
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
    0 references
     
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