DLMF:11.10.E32 (Q4054)

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DLMF:11.10.E32
No description defined

    Statements

    Defining formula
    𝐉 ν - 1 ⁡ ( z ) + 𝐉 ν + 1 ⁡ ( z ) = 2 ⁢ ν z ⁢ 𝐉 ν ⁡ ( z ) - 2 π ⁢ z ⁢ sin ⁡ ( π ⁢ ν ) , Anger-J 𝜈 1 𝑧 Anger-J 𝜈 1 𝑧 2 𝜈 𝑧 Anger-J 𝜈 𝑧 2 𝜋 𝑧 𝜋 𝜈 {\displaystyle{\displaystyle\mathbf{J}_{\nu-1}\left(z\right)+\mathbf{J}_{\nu+1% }\left(z\right)=\frac{2\nu}{z}\mathbf{J}_{\nu}\left(z\right)-\frac{2}{\pi z}% \sin\left(\pi\nu\right),}}
    0 references
    DLMF id
    DLMF:11.10.E32
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    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.m2aqdec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aydec
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    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2aodec
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    Q11491
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C11.S1.XMD2.m1acdec
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    Q11492
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C11.S1.XMD3.m1aadec
    0 references
     
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