DLMF:11.10.E14 (Q4032)

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DLMF:11.10.E14
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    Statements

    Defining formula
    sin ⁡ ( π ⁢ ν ) ⁢ 𝐄 ν ⁡ ( z ) = 𝐉 - ν ⁡ ( z ) - cos ⁡ ( π ⁢ ν ) ⁢ 𝐉 ν ⁡ ( z ) . 𝜋 𝜈 Weber-E 𝜈 𝑧 Anger-J 𝜈 𝑧 𝜋 𝜈 Anger-J 𝜈 𝑧 {\displaystyle{\displaystyle\sin\left(\pi\nu\right)\,\mathbf{E}_{\nu}\left(z% \right)=\mathbf{J}_{-\nu}\left(z\right)-\cos\left(\pi\nu\right)\,\mathbf{J}_{% \nu}\left(z\right).}}
    0 references
    DLMF id
    DLMF:11.10.E14
    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.m2ahdec
    0 references
    Weber function
    Defining formula
    𝐄 ν ⁡ ( z ) Weber-E 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{E}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S10.E2.m2ahdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aidec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2afdec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2agdec
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    Q11491
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C11.S1.XMD2.m1mdec
    0 references
    Q11492
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C11.S1.XMD3.m1qdec
    0 references
     
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