DLMF:11.11.E5 (Q4065): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11492 / rank
 
Normal rank
Property / Symbols used: Q11492 / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11492 / qualifier
 
xml-id: C11.S1.XMD3.m1ddec

Latest revision as of 15:01, 2 January 2020

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DLMF:11.11.E5
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    Statements

    Defining formula
    𝐉 ν ⁡ ( z ) = sin ⁡ ( π ⁢ ν ) π ⁢ ν ⁢ ( 1 - ν ⁢ z ν 2 - 1 + O ⁡ ( 1 ν 2 ) ) , Anger-J 𝜈 𝑧 𝜋 𝜈 𝜋 𝜈 1 𝜈 𝑧 superscript 𝜈 2 1 Big-O 1 superscript 𝜈 2 {\displaystyle{\displaystyle\mathbf{J}_{\nu}\left(z\right)=\frac{\sin\left(\pi% \nu\right)}{\pi\nu}\left(1-\frac{\nu z}{\nu^{2}-1}+O\left(\frac{1}{\nu^{2}}% \right)\right),}}
    0 references
    DLMF id
    DLMF:11.11.E5
    0 references
    Symbols used
    Anger function
    Defining formula
    𝐉 ν ⁡ ( z ) Anger-J 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{J}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S10.E1.m2aadec
    0 references
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2aadec
    0 references
    Q11491
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C11.S1.XMD2.m1cdec
    0 references
    Q11492
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C11.S1.XMD3.m1ddec
    0 references
     
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