DLMF:11.10.E17 (Q4035)

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DLMF:11.10.E17
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    Statements

    Defining formula
    𝐉 ν ⁡ ( z ) = sin ⁡ ( π ⁢ ν ) π ⁢ ( s 0 , ν ⁡ ( z ) - ν ⁢ s - 1 , ν ⁡ ( z ) ) , Anger-J 𝜈 𝑧 𝜋 𝜈 𝜋 Lommel-s 0 𝜈 𝑧 𝜈 Lommel-s 1 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{J}_{\nu}\left(z\right)=\frac{\sin\left(\pi% \nu\right)}{\pi}(s_{{0},{\nu}}\left(z\right)-\nu s_{{-1},{\nu}}\left(z\right))% ,}}
    0 references
    DLMF id
    DLMF:11.10.E17
    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.m2ajdec
    0 references
    Lommel function
    Defining formula
    s μ , ν ⁡ ( z ) Lommel-s 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle s_{{\NVar{\mu}},{\NVar{\nu}}}\left(\NVar{z}\right% )}}
    xml-id
    C11.S9.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.m2aldec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2aidec
    0 references
    Q11491
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C11.S1.XMD2.m1pdec
    0 references
     
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