DLMF:11.11.E5 (Q4762)

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DLMF:11.11.E5
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    Statements

    DLMF 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
    Symbols used
    Anger function
    DLMF 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
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    order not exceeding
    DLMF defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2adec
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    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
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    sine function
    DLMF defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2aadec
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    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C11.S1.XMD2.m1cdec
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    real or complex order
    DLMF defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C11.S1.XMD3.m1ddec
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    Identifiers

     
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